%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SYN442-1 : TPTP v9.0.0. Released v2.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:39:07 AM UTC 2025
% Result : Unsatisfiable 0.60s 0.77s
% Output : Proof 0.79s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SYN442-1 : TPTP v9.0.0. Released v2.1.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n016.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 12:36:02 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.60/0.77 % SZS status Unsatisfiable
% 0.60/0.77 % SZS output start Proof
% 0.60/0.77 tff(c3_1_type, type, (
% 0.60/0.77 c3_1: $i > $o)).
% 0.60/0.77 tff(a179_type, type, (
% 0.60/0.77 a179: $i)).
% 0.60/0.77 tff(c2_1_type, type, (
% 0.60/0.77 c2_1: $i > $o)).
% 0.60/0.77 tff(c1_1_type, type, (
% 0.60/0.77 c1_1: $i > $o)).
% 0.60/0.77 tff(ndr1_0_type, type, (
% 0.60/0.77 ndr1_0: $o)).
% 0.60/0.77 tff(a131_type, type, (
% 0.60/0.77 a131: $i)).
% 0.60/0.77 tff(hskp5_type, type, (
% 0.60/0.77 hskp5: $o)).
% 0.60/0.77 tff(c0_1_type, type, (
% 0.60/0.77 c0_1: $i > $o)).
% 0.60/0.77 tff(a149_type, type, (
% 0.60/0.77 a149: $i)).
% 0.60/0.77 tff(a144_type, type, (
% 0.60/0.77 a144: $i)).
% 0.60/0.77 tff(hskp13_type, type, (
% 0.60/0.77 hskp13: $o)).
% 0.60/0.77 tff(a159_type, type, (
% 0.60/0.77 a159: $i)).
% 0.60/0.77 tff(hskp4_type, type, (
% 0.60/0.77 hskp4: $o)).
% 0.60/0.77 tff(a136_type, type, (
% 0.60/0.77 a136: $i)).
% 0.60/0.77 tff(hskp9_type, type, (
% 0.60/0.77 hskp9: $o)).
% 0.60/0.77 tff(a128_type, type, (
% 0.60/0.77 a128: $i)).
% 0.60/0.77 tff(hskp3_type, type, (
% 0.60/0.77 hskp3: $o)).
% 0.60/0.77 tff(a145_type, type, (
% 0.60/0.77 a145: $i)).
% 0.60/0.77 tff(hskp14_type, type, (
% 0.60/0.77 hskp14: $o)).
% 0.60/0.77 tff(a170_type, type, (
% 0.60/0.77 a170: $i)).
% 0.60/0.77 tff(hskp21_type, type, (
% 0.60/0.77 hskp21: $o)).
% 0.60/0.77 tff(hskp6_type, type, (
% 0.60/0.77 hskp6: $o)).
% 0.60/0.77 tff(hskp15_type, type, (
% 0.60/0.77 hskp15: $o)).
% 0.60/0.77 tff(a150_type, type, (
% 0.60/0.77 a150: $i)).
% 0.60/0.77 tff(hskp29_type, type, (
% 0.60/0.77 hskp29: $o)).
% 0.60/0.77 tff(a125_type, type, (
% 0.60/0.77 a125: $i)).
% 0.60/0.77 tff(hskp1_type, type, (
% 0.60/0.77 hskp1: $o)).
% 0.60/0.77 tff(hskp18_type, type, (
% 0.60/0.77 hskp18: $o)).
% 0.60/0.77 tff(a139_type, type, (
% 0.60/0.77 a139: $i)).
% 0.60/0.77 tff(hskp11_type, type, (
% 0.60/0.77 hskp11: $o)).
% 0.60/0.77 tff(a140_type, type, (
% 0.60/0.77 a140: $i)).
% 0.60/0.77 tff(a199_type, type, (
% 0.60/0.77 a199: $i)).
% 0.60/0.77 tff(hskp30_type, type, (
% 0.60/0.77 hskp30: $o)).
% 0.60/0.77 tff(hskp10_type, type, (
% 0.60/0.77 hskp10: $o)).
% 0.60/0.77 tff(a138_type, type, (
% 0.60/0.77 a138: $i)).
% 0.60/0.77 tff(a151_type, type, (
% 0.60/0.77 a151: $i)).
% 0.60/0.77 tff(hskp16_type, type, (
% 0.60/0.77 hskp16: $o)).
% 0.60/0.77 tff(hskp12_type, type, (
% 0.60/0.77 hskp12: $o)).
% 0.60/0.77 tff(a133_type, type, (
% 0.60/0.77 a133: $i)).
% 0.60/0.77 tff(a158_type, type, (
% 0.60/0.77 a158: $i)).
% 0.60/0.77 tff(hskp17_type, type, (
% 0.60/0.77 hskp17: $o)).
% 0.60/0.77 tff(a162_type, type, (
% 0.60/0.77 a162: $i)).
% 0.60/0.77 tff(hskp19_type, type, (
% 0.60/0.77 hskp19: $o)).
% 0.60/0.77 tff(hskp8_type, type, (
% 0.60/0.77 hskp8: $o)).
% 0.60/0.77 tff(a135_type, type, (
% 0.60/0.77 a135: $i)).
% 0.60/0.77 tff(a168_type, type, (
% 0.60/0.77 a168: $i)).
% 0.60/0.77 tff(hskp20_type, type, (
% 0.60/0.77 hskp20: $o)).
% 0.60/0.77 tff(hskp22_type, type, (
% 0.60/0.77 hskp22: $o)).
% 0.60/0.77 tff(a137_type, type, (
% 0.60/0.77 a137: $i)).
% 0.60/0.77 tff(hskp27_type, type, (
% 0.60/0.77 hskp27: $o)).
% 0.60/0.77 tff(a124_type, type, (
% 0.60/0.77 a124: $i)).
% 0.60/0.77 tff(hskp0_type, type, (
% 0.60/0.77 hskp0: $o)).
% 0.60/0.77 tff(a143_type, type, (
% 0.60/0.77 a143: $i)).
% 0.60/0.77 tff(hskp28_type, type, (
% 0.60/0.77 hskp28: $o)).
% 0.60/0.77 tff(a183_type, type, (
% 0.60/0.77 a183: $i)).
% 0.60/0.77 tff(hskp24_type, type, (
% 0.60/0.77 hskp24: $o)).
% 0.60/0.77 tff(a130_type, type, (
% 0.60/0.77 a130: $i)).
% 0.60/0.77 tff(1,plain,
% 0.60/0.77 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W))) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W))))),
% 0.60/0.77 inference(bind,[status(th)],[])).
% 0.60/0.77 tff(2,plain,
% 0.60/0.77 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))),
% 0.60/0.77 inference(quant_intro,[status(thm)],[1])).
% 0.60/0.77 tff(3,plain,
% 0.60/0.77 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))),
% 0.60/0.77 inference(rewrite,[status(thm)],[])).
% 0.60/0.77 tff(4,plain,
% 0.60/0.77 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(W)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(W))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(W)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(W))))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(W))) | c2_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c2_1(W))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c2_1(W)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(W))) | c2_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c2_1(W))))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(W))) | c2_1(U)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c2_1(W))) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c2_1(W))) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | (~c2_1(W)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(W))) | c2_1(U)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | (~c2_1(W))))), ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(W))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | c1_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | (~c2_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | (~c2_1(W))) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | (~c2_1(W)))), ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(W))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | c1_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | (~c2_1(W))))), (((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(W))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | c1_1(W)) | c3_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | (~c2_1(W))) | c3_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | (~c2_1(W))) | c3_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))), (((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(W))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | c1_1(W)) | c3_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))))),
% 0.60/0.77 inference(bind,[status(th)],[])).
% 0.60/0.77 tff(5,plain,
% 0.60/0.77 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(W))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | c1_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))),
% 0.60/0.77 inference(quant_intro,[status(thm)],[4])).
% 0.60/0.77 tff(6,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(W))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | c1_1(W)) | c3_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause181')).
% 0.60/0.77 tff(7,plain,
% 0.60/0.77 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[6, 5])).
% 0.60/0.78 tff(8,plain,
% 0.60/0.78 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[7, 3])).
% 0.60/0.78 tff(9,plain,(
% 0.60/0.78 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))),
% 0.60/0.78 inference(skolemize,[status(sab)],[8])).
% 0.60/0.78 tff(10,plain,
% 0.60/0.78 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[9, 2])).
% 0.60/0.78 tff(11,assumption,(~hskp13), introduced(assumption)).
% 0.60/0.78 tff(12,plain,
% 0.60/0.78 (^[V: $i, U: $i] : refl((hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V))))),
% 0.60/0.78 inference(bind,[status(th)],[])).
% 0.60/0.78 tff(13,plain,
% 0.60/0.78 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 0.60/0.78 inference(quant_intro,[status(thm)],[12])).
% 0.60/0.78 tff(14,plain,
% 0.60/0.78 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(15,plain,
% 0.60/0.78 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) <=> ((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c1_1(V)) | (~c0_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(V)) | hskp13) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V))) | hskp13))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V))) | hskp13) <=> (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(V)) | hskp13) <=> (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))))),
% 0.60/0.78 inference(bind,[status(th)],[])).
% 0.60/0.78 tff(16,plain,
% 0.60/0.78 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(V)) | hskp13) <=> ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 0.60/0.78 inference(quant_intro,[status(thm)],[15])).
% 0.60/0.78 tff(17,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | c3_1(V)) | hskp13)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause177')).
% 0.60/0.78 tff(18,plain,
% 0.60/0.78 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[17, 16])).
% 0.60/0.78 tff(19,plain,
% 0.60/0.78 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[18, 14])).
% 0.60/0.78 tff(20,plain,(
% 0.60/0.78 ![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 0.60/0.78 inference(skolemize,[status(sab)],[19])).
% 0.60/0.78 tff(21,plain,
% 0.60/0.78 (![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[20, 13])).
% 0.60/0.78 tff(22,plain,
% 0.60/0.78 (^[V: $i, U: $i] : refl((hskp9 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)) <=> (hskp9 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)))),
% 0.60/0.78 inference(bind,[status(th)],[])).
% 0.60/0.78 tff(23,plain,
% 0.60/0.78 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))),
% 0.60/0.78 inference(quant_intro,[status(thm)],[22])).
% 0.60/0.78 tff(24,plain,
% 0.60/0.78 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(25,plain,
% 0.60/0.78 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U))))), (((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))), (((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U))))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V)))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V)))), ((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))), ((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)))), (((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp9) <=> (((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)) | hskp9))), rewrite((((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)) | hskp9) <=> (hskp9 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))), (((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp9) <=> (hskp9 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))))),
% 0.60/0.78 inference(bind,[status(th)],[])).
% 0.60/0.78 tff(26,plain,
% 0.60/0.78 (![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp9) <=> ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))),
% 0.60/0.78 inference(quant_intro,[status(thm)],[25])).
% 0.60/0.78 tff(27,axiom,(![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause160')).
% 0.60/0.78 tff(28,plain,
% 0.60/0.78 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[27, 26])).
% 0.60/0.78 tff(29,plain,
% 0.60/0.78 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[28, 24])).
% 0.60/0.78 tff(30,plain,(
% 0.60/0.78 ![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))),
% 0.60/0.78 inference(skolemize,[status(sab)],[29])).
% 0.60/0.78 tff(31,plain,
% 0.60/0.78 (![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[30, 23])).
% 0.60/0.78 tff(32,plain,
% 0.60/0.78 (^[V: $i, U: $i] : refl((hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) <=> (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))))),
% 0.60/0.78 inference(bind,[status(th)],[])).
% 0.60/0.78 tff(33,plain,
% 0.60/0.78 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.60/0.78 inference(quant_intro,[status(thm)],[32])).
% 0.60/0.78 tff(34,plain,
% 0.60/0.78 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(35,plain,
% 0.60/0.78 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(V)))), ((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(V))))), (((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(V)))), (((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(V))))), ((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c2_1(U)) | (~c3_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | (~c3_1(V)))), ((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | (~c3_1(V))))), (((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | (~c3_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | (~c3_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V)))), (((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V))))), ((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))), ((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))))), (((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp3) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) | hskp3))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V))) | hskp3) <=> (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))), (((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp3) <=> (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))))),
% 0.60/0.78 inference(bind,[status(th)],[])).
% 0.60/0.78 tff(36,plain,
% 0.60/0.78 (![V: $i, U: $i] : ((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp3) <=> ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.60/0.78 inference(quant_intro,[status(thm)],[35])).
% 0.60/0.78 tff(37,axiom,(![V: $i, U: $i] : ((((((((~c2_1(U)) | (~ndr1_0)) | (~c3_1(V))) | c1_1(U)) | c3_1(U)) | c0_1(V)) | c2_1(V)) | hskp3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause162')).
% 0.60/0.78 tff(38,plain,
% 0.60/0.78 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.60/0.78 tff(39,plain,
% 0.60/0.78 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[38, 34])).
% 0.60/0.78 tff(40,plain,(
% 0.60/0.78 ![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.60/0.78 inference(skolemize,[status(sab)],[39])).
% 0.60/0.78 tff(41,plain,
% 0.60/0.78 (![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[40, 33])).
% 0.60/0.78 tff(42,plain,
% 0.60/0.78 (^[U: $i] : refl((hskp14 | hskp3 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U))) <=> (hskp14 | hskp3 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U))))),
% 0.60/0.78 inference(bind,[status(th)],[])).
% 0.60/0.78 tff(43,plain,
% 0.60/0.78 (![U: $i] : (hskp14 | hskp3 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp14 | hskp3 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))),
% 0.60/0.78 inference(quant_intro,[status(thm)],[42])).
% 0.60/0.78 tff(44,plain,
% 0.60/0.78 (![U: $i] : (hskp14 | hskp3 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp14 | hskp3 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(45,plain,
% 0.60/0.78 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U))))), (((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))), (((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U))))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp14) <=> (((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U))) | hskp14))), rewrite((((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U))) | hskp14) <=> (hskp14 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp14) <=> (hskp14 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U))))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp14) | hskp3) <=> ((hskp14 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U))) | hskp3))), rewrite(((hskp14 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U))) | hskp3) <=> (hskp14 | hskp3 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp14) | hskp3) <=> (hskp14 | hskp3 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))))),
% 0.60/0.78 inference(bind,[status(th)],[])).
% 0.60/0.78 tff(46,plain,
% 0.60/0.78 (![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp14) | hskp3) <=> ![U: $i] : (hskp14 | hskp3 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))),
% 0.60/0.78 inference(quant_intro,[status(thm)],[45])).
% 0.60/0.78 tff(47,axiom,(![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp14) | hskp3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause138')).
% 0.60/0.78 tff(48,plain,
% 0.60/0.78 (![U: $i] : (hskp14 | hskp3 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[47, 46])).
% 0.60/0.78 tff(49,plain,
% 0.60/0.78 (![U: $i] : (hskp14 | hskp3 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[48, 44])).
% 0.60/0.78 tff(50,plain,(
% 0.60/0.78 ![U: $i] : (hskp14 | hskp3 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))),
% 0.60/0.78 inference(skolemize,[status(sab)],[49])).
% 0.60/0.78 tff(51,plain,
% 0.60/0.78 (![U: $i] : (hskp14 | hskp3 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[50, 43])).
% 0.60/0.78 tff(52,assumption,(~hskp3), introduced(assumption)).
% 0.60/0.78 tff(53,assumption,(~hskp21), introduced(assumption)).
% 0.60/0.78 tff(54,plain,
% 0.60/0.78 (^[U: $i] : refl((hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))))),
% 0.60/0.78 inference(bind,[status(th)],[])).
% 0.60/0.78 tff(55,plain,
% 0.60/0.78 (![U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.60/0.78 inference(quant_intro,[status(thm)],[54])).
% 0.60/0.78 tff(56,plain,
% 0.60/0.78 (![U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(57,plain,
% 0.60/0.78 (^[U: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp15) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp15))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp15) <=> (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp15) <=> (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))))),
% 0.60/0.78 inference(bind,[status(th)],[])).
% 0.60/0.78 tff(58,plain,
% 0.60/0.78 (![U: $i] : (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp15) <=> ![U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.60/0.78 inference(quant_intro,[status(thm)],[57])).
% 0.60/0.78 tff(59,axiom,(![U: $i] : (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp15)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause147')).
% 0.60/0.78 tff(60,plain,
% 0.60/0.78 (![U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[59, 58])).
% 0.60/0.78 tff(61,plain,
% 0.60/0.78 (![U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[60, 56])).
% 0.60/0.78 tff(62,plain,(
% 0.60/0.78 ![U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.60/0.78 inference(skolemize,[status(sab)],[61])).
% 0.60/0.78 tff(63,plain,
% 0.60/0.78 (![U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[62, 55])).
% 0.60/0.78 tff(64,plain,
% 0.60/0.78 (^[U: $i] : refl((hskp29 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))) <=> (hskp29 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))))),
% 0.60/0.78 inference(bind,[status(th)],[])).
% 0.60/0.78 tff(65,plain,
% 0.60/0.78 (![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.60/0.78 inference(quant_intro,[status(thm)],[64])).
% 0.60/0.78 tff(66,plain,
% 0.60/0.78 (![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(67,plain,
% 0.60/0.78 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U))))), (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))), (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp29) <=> (((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))) | hskp29))), rewrite((((~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))) | hskp29) <=> (hskp29 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp29) <=> (hskp29 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp29) | hskp3) <=> ((hskp29 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))) | hskp3))), rewrite(((hskp29 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U))) | hskp3) <=> (hskp29 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp29) | hskp3) <=> (hskp29 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))))),
% 0.60/0.78 inference(bind,[status(th)],[])).
% 0.60/0.78 tff(68,plain,
% 0.60/0.78 (![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp29) | hskp3) <=> ![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.60/0.78 inference(quant_intro,[status(thm)],[67])).
% 0.60/0.78 tff(69,axiom,(![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp29) | hskp3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause140')).
% 0.60/0.78 tff(70,plain,
% 0.60/0.78 (![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[69, 68])).
% 0.60/0.78 tff(71,plain,
% 0.60/0.78 (![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[70, 66])).
% 0.60/0.78 tff(72,plain,(
% 0.60/0.78 ![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.60/0.78 inference(skolemize,[status(sab)],[71])).
% 0.60/0.78 tff(73,plain,
% 0.60/0.78 (![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[72, 65])).
% 0.60/0.78 tff(74,assumption,(~hskp15), introduced(assumption)).
% 0.60/0.78 tff(75,plain,
% 0.60/0.78 (^[U: $i] : refl((hskp3 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))) <=> (hskp3 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))))),
% 0.60/0.78 inference(bind,[status(th)],[])).
% 0.60/0.78 tff(76,plain,
% 0.60/0.78 (![U: $i] : (hskp3 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp3 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))),
% 0.60/0.78 inference(quant_intro,[status(thm)],[75])).
% 0.60/0.78 tff(77,plain,
% 0.60/0.78 (![U: $i] : (hskp3 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp3 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(78,plain,
% 0.60/0.78 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c0_1(U))))), (((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c0_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c0_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))), (((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))))), ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp1) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))) | hskp1))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))) | hskp1) <=> (hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))), ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp1) <=> (hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))))), (((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp1) | hskp3) <=> ((hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))) | hskp3))), rewrite(((hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U))) | hskp3) <=> (hskp3 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))), (((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp1) | hskp3) <=> (hskp3 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))))),
% 0.60/0.78 inference(bind,[status(th)],[])).
% 0.60/0.78 tff(79,plain,
% 0.60/0.78 (![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp1) | hskp3) <=> ![U: $i] : (hskp3 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))),
% 0.60/0.78 inference(quant_intro,[status(thm)],[78])).
% 0.60/0.78 tff(80,axiom,(![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp1) | hskp3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause145')).
% 0.60/0.78 tff(81,plain,
% 0.60/0.78 (![U: $i] : (hskp3 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[80, 79])).
% 0.60/0.78 tff(82,plain,
% 0.60/0.78 (![U: $i] : (hskp3 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[81, 77])).
% 0.60/0.78 tff(83,plain,(
% 0.60/0.78 ![U: $i] : (hskp3 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))),
% 0.60/0.78 inference(skolemize,[status(sab)],[82])).
% 0.60/0.78 tff(84,plain,
% 0.60/0.78 (![U: $i] : (hskp3 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))),
% 0.60/0.78 inference(modus_ponens,[status(thm)],[83, 76])).
% 0.60/0.78 tff(85,plain,
% 0.60/0.78 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W))))),
% 0.60/0.78 inference(bind,[status(th)],[])).
% 0.60/0.78 tff(86,plain,
% 0.60/0.78 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))),
% 0.60/0.78 inference(quant_intro,[status(thm)],[85])).
% 0.60/0.78 tff(87,plain,
% 0.60/0.78 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))),
% 0.60/0.78 inference(rewrite,[status(thm)],[])).
% 0.60/0.78 tff(88,plain,
% 0.60/0.78 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(W)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(W))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(W))) | c2_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(W)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(W))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(W))))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(W))) | c2_1(V)) | c1_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | (~c2_1(W))) | c1_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W)))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(W))) | c2_1(V)) | c1_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W))))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(W))) | c2_1(V)) | c1_1(W)) | c3_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W))) | c3_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | (~c2_1(W))) | c3_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(W))) | c2_1(V)) | c1_1(W)) | c3_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))))),
% 0.60/0.79 inference(bind,[status(th)],[])).
% 0.60/0.79 tff(89,plain,
% 0.60/0.79 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(W))) | c2_1(V)) | c1_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))),
% 0.60/0.79 inference(quant_intro,[status(thm)],[88])).
% 0.60/0.79 tff(90,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c1_1(V))) | (~c2_1(W))) | c2_1(V)) | c1_1(W)) | c3_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause184')).
% 0.60/0.79 tff(91,plain,
% 0.60/0.79 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[90, 89])).
% 0.60/0.79 tff(92,plain,
% 0.60/0.79 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[91, 87])).
% 0.60/0.79 tff(93,plain,(
% 0.60/0.79 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))),
% 0.60/0.79 inference(skolemize,[status(sab)],[92])).
% 0.60/0.79 tff(94,plain,
% 0.60/0.79 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[93, 86])).
% 0.60/0.79 tff(95,assumption,(~hskp18), introduced(assumption)).
% 0.60/0.79 tff(96,assumption,(hskp10), introduced(assumption)).
% 0.60/0.79 tff(97,plain,
% 0.60/0.79 (((~hskp10) | (~c1_1(a138))) <=> ((~hskp10) | (~c1_1(a138)))),
% 0.60/0.79 inference(rewrite,[status(thm)],[])).
% 0.60/0.79 tff(98,plain,
% 0.60/0.79 (((~c1_1(a138)) | (~hskp10)) <=> ((~hskp10) | (~c1_1(a138)))),
% 0.60/0.79 inference(rewrite,[status(thm)],[])).
% 0.60/0.79 tff(99,axiom,((~c1_1(a138)) | (~hskp10)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause113')).
% 0.60/0.79 tff(100,plain,
% 0.60/0.79 ((~hskp10) | (~c1_1(a138))),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[99, 98])).
% 0.60/0.79 tff(101,plain,
% 0.60/0.79 ((~hskp10) | (~c1_1(a138))),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[100, 97])).
% 0.60/0.79 tff(102,plain,
% 0.60/0.79 (~c1_1(a138)),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[101, 96])).
% 0.60/0.79 tff(103,plain,
% 0.60/0.79 (((~hskp10) | c3_1(a138)) <=> ((~hskp10) | c3_1(a138))),
% 0.60/0.79 inference(rewrite,[status(thm)],[])).
% 0.60/0.79 tff(104,axiom,((~hskp10) | c3_1(a138)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause69')).
% 0.60/0.79 tff(105,plain,
% 0.60/0.79 ((~hskp10) | c3_1(a138)),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[104, 103])).
% 0.60/0.79 tff(106,plain,
% 0.60/0.79 ((~hskp10) | c3_1(a138)),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[105, 103])).
% 0.60/0.79 tff(107,plain,
% 0.60/0.79 ((~hskp10) | c3_1(a138)),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[106, 103])).
% 0.60/0.79 tff(108,plain,
% 0.60/0.79 ((~hskp10) | c3_1(a138)),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[107, 103])).
% 0.60/0.79 tff(109,plain,
% 0.60/0.79 ((~hskp10) | c3_1(a138)),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[108, 103])).
% 0.60/0.79 tff(110,plain,
% 0.60/0.79 (c3_1(a138)),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[109, 96])).
% 0.60/0.79 tff(111,plain,
% 0.60/0.79 (((~hskp10) | c0_1(a138)) <=> ((~hskp10) | c0_1(a138))),
% 0.60/0.79 inference(rewrite,[status(thm)],[])).
% 0.60/0.79 tff(112,axiom,((~hskp10) | c0_1(a138)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause68')).
% 0.60/0.79 tff(113,plain,
% 0.60/0.79 ((~hskp10) | c0_1(a138)),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[112, 111])).
% 0.60/0.79 tff(114,plain,
% 0.60/0.79 ((~hskp10) | c0_1(a138)),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[113, 111])).
% 0.60/0.79 tff(115,plain,
% 0.60/0.79 ((~hskp10) | c0_1(a138)),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[114, 111])).
% 0.60/0.79 tff(116,plain,
% 0.60/0.79 ((~hskp10) | c0_1(a138)),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[115, 111])).
% 0.60/0.79 tff(117,plain,
% 0.60/0.79 ((~hskp10) | c0_1(a138)),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[116, 111])).
% 0.60/0.79 tff(118,plain,
% 0.60/0.79 (c0_1(a138)),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[117, 96])).
% 0.60/0.79 tff(119,plain,
% 0.60/0.79 (^[U: $i] : refl((hskp21 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U))) <=> (hskp21 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U))))),
% 0.60/0.79 inference(bind,[status(th)],[])).
% 0.60/0.79 tff(120,plain,
% 0.60/0.79 (![U: $i] : (hskp21 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp21 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))),
% 0.60/0.79 inference(quant_intro,[status(thm)],[119])).
% 0.60/0.79 tff(121,plain,
% 0.60/0.79 (![U: $i] : (hskp21 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp21 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))),
% 0.60/0.79 inference(rewrite,[status(thm)],[])).
% 0.60/0.79 tff(122,plain,
% 0.60/0.79 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U))))), (((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))), (((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U))))), ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp18) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U))) | hskp18))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U))) | hskp18) <=> (hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))), ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp18) <=> (hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U))))), (((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp18) | hskp21) <=> ((hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U))) | hskp21))), rewrite(((hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U))) | hskp21) <=> (hskp21 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))), (((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp18) | hskp21) <=> (hskp21 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))))),
% 0.60/0.79 inference(bind,[status(th)],[])).
% 0.60/0.79 tff(123,plain,
% 0.60/0.79 (![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp18) | hskp21) <=> ![U: $i] : (hskp21 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))),
% 0.60/0.79 inference(quant_intro,[status(thm)],[122])).
% 0.60/0.79 tff(124,axiom,(![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c2_1(U)) | c3_1(U)) | hskp18) | hskp21)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause146')).
% 0.60/0.79 tff(125,plain,
% 0.60/0.79 (![U: $i] : (hskp21 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[124, 123])).
% 0.60/0.79 tff(126,plain,
% 0.60/0.79 (![U: $i] : (hskp21 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[125, 121])).
% 0.60/0.79 tff(127,plain,(
% 0.60/0.79 ![U: $i] : (hskp21 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))),
% 0.60/0.79 inference(skolemize,[status(sab)],[126])).
% 0.60/0.79 tff(128,plain,
% 0.60/0.79 (![U: $i] : (hskp21 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[127, 120])).
% 0.60/0.79 tff(129,plain,
% 0.60/0.79 (^[U: $i] : refl((hskp21 | hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> (hskp21 | hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))))),
% 0.60/0.79 inference(bind,[status(th)],[])).
% 0.60/0.79 tff(130,plain,
% 0.60/0.79 (![U: $i] : (hskp21 | hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp21 | hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.60/0.79 inference(quant_intro,[status(thm)],[129])).
% 0.60/0.79 tff(131,plain,
% 0.60/0.79 (![U: $i] : (hskp21 | hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp21 | hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.60/0.79 inference(rewrite,[status(thm)],[])).
% 0.60/0.79 tff(132,plain,
% 0.60/0.79 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp16) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp16))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp16) <=> (hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp16) <=> (hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp16) | hskp21) <=> ((hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp21))), rewrite(((hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp21) <=> (hskp21 | hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp16) | hskp21) <=> (hskp21 | hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))))),
% 0.60/0.79 inference(bind,[status(th)],[])).
% 0.60/0.79 tff(133,plain,
% 0.60/0.79 (![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp16) | hskp21) <=> ![U: $i] : (hskp21 | hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.60/0.79 inference(quant_intro,[status(thm)],[132])).
% 0.60/0.79 tff(134,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp16) | hskp21)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause149')).
% 0.60/0.79 tff(135,plain,
% 0.60/0.79 (![U: $i] : (hskp21 | hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[134, 133])).
% 0.60/0.79 tff(136,plain,
% 0.60/0.79 (![U: $i] : (hskp21 | hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[135, 131])).
% 0.60/0.79 tff(137,plain,(
% 0.60/0.79 ![U: $i] : (hskp21 | hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.60/0.79 inference(skolemize,[status(sab)],[136])).
% 0.60/0.79 tff(138,plain,
% 0.60/0.79 (![U: $i] : (hskp21 | hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[137, 130])).
% 0.60/0.79 tff(139,assumption,(~c1_1(a138)), introduced(assumption)).
% 0.60/0.79 tff(140,assumption,(c3_1(a138)), introduced(assumption)).
% 0.60/0.79 tff(141,assumption,(c0_1(a138)), introduced(assumption)).
% 0.60/0.79 tff(142,assumption,(~ndr1_0), introduced(assumption)).
% 0.60/0.79 tff(143,plain,
% 0.60/0.79 ((ndr1_0 | (~hskp10)) <=> (ndr1_0 | (~hskp10))),
% 0.60/0.79 inference(rewrite,[status(thm)],[])).
% 0.60/0.79 tff(144,plain,
% 0.60/0.79 (((~hskp10) | ndr1_0) <=> (ndr1_0 | (~hskp10))),
% 0.60/0.79 inference(rewrite,[status(thm)],[])).
% 0.60/0.79 tff(145,axiom,((~hskp10) | ndr1_0), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause22')).
% 0.60/0.79 tff(146,plain,
% 0.60/0.79 (ndr1_0 | (~hskp10)),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[145, 144])).
% 0.60/0.79 tff(147,plain,
% 0.60/0.79 (ndr1_0 | (~hskp10)),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[146, 143])).
% 0.60/0.79 tff(148,plain,
% 0.60/0.79 (~hskp10),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[147, 142])).
% 0.60/0.79 tff(149,plain,
% 0.60/0.79 (((~hskp30) | ndr1_0) <=> ((~hskp30) | ndr1_0)),
% 0.60/0.79 inference(rewrite,[status(thm)],[])).
% 0.60/0.79 tff(150,axiom,((~hskp30) | ndr1_0), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause2')).
% 0.60/0.79 tff(151,plain,
% 0.60/0.79 ((~hskp30) | ndr1_0),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[150, 149])).
% 0.60/0.79 tff(152,plain,
% 0.60/0.79 ((~hskp30) | ndr1_0),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[151, 149])).
% 0.60/0.79 tff(153,plain,
% 0.60/0.79 ((~hskp30) | ndr1_0),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[152, 149])).
% 0.60/0.79 tff(154,plain,
% 0.60/0.79 ((~hskp30) | ndr1_0),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[153, 149])).
% 0.60/0.79 tff(155,plain,
% 0.60/0.79 ((~hskp30) | ndr1_0),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[154, 149])).
% 0.60/0.79 tff(156,plain,
% 0.60/0.79 (~hskp30),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[155, 142])).
% 0.60/0.79 tff(157,plain,
% 0.60/0.79 ((ndr1_0 | (~hskp18)) <=> (ndr1_0 | (~hskp18))),
% 0.60/0.79 inference(rewrite,[status(thm)],[])).
% 0.60/0.79 tff(158,plain,
% 0.60/0.79 (((~hskp18) | ndr1_0) <=> (ndr1_0 | (~hskp18))),
% 0.60/0.79 inference(rewrite,[status(thm)],[])).
% 0.60/0.79 tff(159,axiom,((~hskp18) | ndr1_0), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause14')).
% 0.60/0.79 tff(160,plain,
% 0.60/0.79 (ndr1_0 | (~hskp18)),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[159, 158])).
% 0.60/0.79 tff(161,plain,
% 0.60/0.79 (ndr1_0 | (~hskp18)),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[160, 157])).
% 0.60/0.79 tff(162,plain,
% 0.60/0.79 (~hskp18),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[161, 142])).
% 0.60/0.79 tff(163,plain,
% 0.60/0.79 ((hskp30 | hskp18 | hskp10) <=> (hskp30 | hskp18 | hskp10)),
% 0.60/0.79 inference(rewrite,[status(thm)],[])).
% 0.60/0.79 tff(164,plain,
% 0.60/0.79 (((hskp30 | hskp10) | hskp18) <=> (hskp30 | hskp18 | hskp10)),
% 0.60/0.79 inference(rewrite,[status(thm)],[])).
% 0.60/0.79 tff(165,plain,
% 0.60/0.79 ((hskp30 | hskp10) <=> (hskp30 | hskp10)),
% 0.60/0.79 inference(rewrite,[status(thm)],[])).
% 0.60/0.79 tff(166,plain,
% 0.60/0.79 (((hskp30 | hskp10) | hskp18) <=> ((hskp30 | hskp10) | hskp18)),
% 0.60/0.79 inference(monotonicity,[status(thm)],[165])).
% 0.60/0.79 tff(167,plain,
% 0.60/0.79 (((hskp30 | hskp10) | hskp18) <=> (hskp30 | hskp18 | hskp10)),
% 0.60/0.79 inference(transitivity,[status(thm)],[166, 164])).
% 0.60/0.79 tff(168,axiom,((hskp30 | hskp10) | hskp18), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause33')).
% 0.60/0.79 tff(169,plain,
% 0.60/0.79 (hskp30 | hskp18 | hskp10),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[168, 167])).
% 0.60/0.79 tff(170,plain,
% 0.60/0.79 (hskp30 | hskp18 | hskp10),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[169, 163])).
% 0.60/0.79 tff(171,plain,
% 0.60/0.79 (hskp30 | hskp18 | hskp10),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[170, 163])).
% 0.60/0.79 tff(172,plain,
% 0.60/0.79 (hskp30 | hskp18 | hskp10),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[171, 163])).
% 0.60/0.79 tff(173,plain,
% 0.60/0.79 (hskp30 | hskp18 | hskp10),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[172, 163])).
% 0.60/0.79 tff(174,plain,
% 0.60/0.79 ($false),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[173, 162, 156, 148])).
% 0.60/0.79 tff(175,plain,(ndr1_0), inference(lemma,lemma(discharge,[]))).
% 0.60/0.79 tff(176,plain,
% 0.60/0.79 (((~![U: $i] : (hskp21 | hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp21 | hskp16 | c1_1(a138) | (~ndr1_0) | (~c3_1(a138)) | (~c0_1(a138)))) <=> ((~![U: $i] : (hskp21 | hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp21 | hskp16 | c1_1(a138) | (~ndr1_0) | (~c3_1(a138)) | (~c0_1(a138)))),
% 0.60/0.79 inference(rewrite,[status(thm)],[])).
% 0.60/0.79 tff(177,plain,
% 0.60/0.79 ((hskp21 | hskp16 | (~ndr1_0) | c1_1(a138) | (~c3_1(a138)) | (~c0_1(a138))) <=> (hskp21 | hskp16 | c1_1(a138) | (~ndr1_0) | (~c3_1(a138)) | (~c0_1(a138)))),
% 0.60/0.79 inference(rewrite,[status(thm)],[])).
% 0.60/0.79 tff(178,plain,
% 0.60/0.79 (((~![U: $i] : (hskp21 | hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp21 | hskp16 | (~ndr1_0) | c1_1(a138) | (~c3_1(a138)) | (~c0_1(a138)))) <=> ((~![U: $i] : (hskp21 | hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp21 | hskp16 | c1_1(a138) | (~ndr1_0) | (~c3_1(a138)) | (~c0_1(a138))))),
% 0.60/0.79 inference(monotonicity,[status(thm)],[177])).
% 0.60/0.79 tff(179,plain,
% 0.60/0.79 (((~![U: $i] : (hskp21 | hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp21 | hskp16 | (~ndr1_0) | c1_1(a138) | (~c3_1(a138)) | (~c0_1(a138)))) <=> ((~![U: $i] : (hskp21 | hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp21 | hskp16 | c1_1(a138) | (~ndr1_0) | (~c3_1(a138)) | (~c0_1(a138)))),
% 0.60/0.79 inference(transitivity,[status(thm)],[178, 176])).
% 0.60/0.79 tff(180,plain,
% 0.60/0.79 ((~![U: $i] : (hskp21 | hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp21 | hskp16 | (~ndr1_0) | c1_1(a138) | (~c3_1(a138)) | (~c0_1(a138)))),
% 0.60/0.79 inference(quant_inst,[status(thm)],[])).
% 0.60/0.79 tff(181,plain,
% 0.60/0.79 ((~![U: $i] : (hskp21 | hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp21 | hskp16 | c1_1(a138) | (~ndr1_0) | (~c3_1(a138)) | (~c0_1(a138))),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[180, 179])).
% 0.60/0.79 tff(182,plain,
% 0.60/0.79 (hskp21 | hskp16),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[181, 175, 141, 140, 139, 138])).
% 0.60/0.79 tff(183,plain,
% 0.60/0.79 (hskp16),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[182, 53])).
% 0.60/0.79 tff(184,plain,
% 0.60/0.79 (((~hskp16) | (~c2_1(a151))) <=> ((~hskp16) | (~c2_1(a151)))),
% 0.60/0.79 inference(rewrite,[status(thm)],[])).
% 0.60/0.79 tff(185,plain,
% 0.60/0.79 (((~c2_1(a151)) | (~hskp16)) <=> ((~hskp16) | (~c2_1(a151)))),
% 0.60/0.79 inference(rewrite,[status(thm)],[])).
% 0.60/0.79 tff(186,axiom,((~c2_1(a151)) | (~hskp16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause102')).
% 0.60/0.79 tff(187,plain,
% 0.60/0.79 ((~hskp16) | (~c2_1(a151))),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[186, 185])).
% 0.60/0.79 tff(188,plain,
% 0.60/0.79 ((~hskp16) | (~c2_1(a151))),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[187, 184])).
% 0.60/0.79 tff(189,plain,
% 0.60/0.79 (~c2_1(a151)),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[188, 183])).
% 0.60/0.79 tff(190,plain,
% 0.60/0.79 (((~hskp16) | c1_1(a151)) <=> ((~hskp16) | c1_1(a151))),
% 0.60/0.79 inference(rewrite,[status(thm)],[])).
% 0.60/0.79 tff(191,axiom,((~hskp16) | c1_1(a151)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause62')).
% 0.60/0.79 tff(192,plain,
% 0.60/0.79 ((~hskp16) | c1_1(a151)),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[191, 190])).
% 0.60/0.79 tff(193,plain,
% 0.60/0.79 ((~hskp16) | c1_1(a151)),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[192, 190])).
% 0.60/0.79 tff(194,plain,
% 0.60/0.79 ((~hskp16) | c1_1(a151)),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[193, 190])).
% 0.60/0.79 tff(195,plain,
% 0.60/0.79 ((~hskp16) | c1_1(a151)),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[194, 190])).
% 0.60/0.79 tff(196,plain,
% 0.60/0.79 ((~hskp16) | c1_1(a151)),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[195, 190])).
% 0.60/0.79 tff(197,plain,
% 0.60/0.79 (c1_1(a151)),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[196, 183])).
% 0.60/0.79 tff(198,plain,
% 0.60/0.79 (((~![U: $i] : (hskp21 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp21 | hskp18 | c2_1(a151) | (~ndr1_0) | c3_1(a151) | (~c1_1(a151)))) <=> ((~![U: $i] : (hskp21 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | hskp21 | hskp18 | c2_1(a151) | (~ndr1_0) | c3_1(a151) | (~c1_1(a151)))),
% 0.60/0.79 inference(rewrite,[status(thm)],[])).
% 0.60/0.79 tff(199,plain,
% 0.60/0.79 ((hskp21 | hskp18 | (~ndr1_0) | c3_1(a151) | c2_1(a151) | (~c1_1(a151))) <=> (hskp21 | hskp18 | c2_1(a151) | (~ndr1_0) | c3_1(a151) | (~c1_1(a151)))),
% 0.60/0.79 inference(rewrite,[status(thm)],[])).
% 0.60/0.79 tff(200,plain,
% 0.60/0.79 (((~![U: $i] : (hskp21 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp21 | hskp18 | (~ndr1_0) | c3_1(a151) | c2_1(a151) | (~c1_1(a151)))) <=> ((~![U: $i] : (hskp21 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp21 | hskp18 | c2_1(a151) | (~ndr1_0) | c3_1(a151) | (~c1_1(a151))))),
% 0.60/0.79 inference(monotonicity,[status(thm)],[199])).
% 0.60/0.79 tff(201,plain,
% 0.60/0.79 (((~![U: $i] : (hskp21 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp21 | hskp18 | (~ndr1_0) | c3_1(a151) | c2_1(a151) | (~c1_1(a151)))) <=> ((~![U: $i] : (hskp21 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | hskp21 | hskp18 | c2_1(a151) | (~ndr1_0) | c3_1(a151) | (~c1_1(a151)))),
% 0.60/0.79 inference(transitivity,[status(thm)],[200, 198])).
% 0.60/0.79 tff(202,plain,
% 0.60/0.79 ((~![U: $i] : (hskp21 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp21 | hskp18 | (~ndr1_0) | c3_1(a151) | c2_1(a151) | (~c1_1(a151)))),
% 0.60/0.79 inference(quant_inst,[status(thm)],[])).
% 0.60/0.79 tff(203,plain,
% 0.60/0.79 ((~![U: $i] : (hskp21 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | hskp21 | hskp18 | c2_1(a151) | (~ndr1_0) | c3_1(a151) | (~c1_1(a151))),
% 0.60/0.79 inference(modus_ponens,[status(thm)],[202, 201])).
% 0.60/0.79 tff(204,plain,
% 0.60/0.79 (c3_1(a151)),
% 0.60/0.79 inference(unit_resolution,[status(thm)],[203, 175, 53, 95, 197, 189, 128])).
% 0.60/0.79 tff(205,plain,
% 0.60/0.79 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W))) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W))))),
% 0.60/0.79 inference(bind,[status(th)],[])).
% 0.60/0.79 tff(206,plain,
% 0.60/0.79 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))),
% 0.60/0.79 inference(quant_intro,[status(thm)],[205])).
% 0.60/0.79 tff(207,plain,
% 0.60/0.79 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))),
% 0.60/0.79 inference(rewrite,[status(thm)],[])).
% 0.60/0.79 tff(208,plain,
% 0.60/0.79 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V))) | (~c2_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(W)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(W))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(W))) | (~c3_1(W))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(W))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(W)) | (~c3_1(W)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(W)) | (~c3_1(W))))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(W)) | (~c3_1(W))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(W)) | (~c3_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(W)) | (~c3_1(W)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(W)) | (~c3_1(W))))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(W)) | (~c3_1(W))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c2_1(W)) | (~c3_1(W))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(W)) | (~c3_1(W)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(W)) | (~c3_1(W))))), ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(W)) | (~c3_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c3_1(V)) | (~c2_1(W)) | (~c3_1(W))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | (~c2_1(W)) | (~c3_1(W)))), ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | (~c2_1(W)) | (~c3_1(W))))), (((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | (~c2_1(W)) | (~c3_1(W))) | c0_1(W)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | (~c2_1(W)) | (~c3_1(W))) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))), (((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))))),
% 0.60/0.79 inference(bind,[status(th)],[])).
% 0.60/0.80 tff(209,plain,
% 0.60/0.80 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))),
% 0.60/0.80 inference(quant_intro,[status(thm)],[208])).
% 0.60/0.80 tff(210,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c3_1(V))) | (~c2_1(W))) | (~c3_1(W))) | c2_1(U)) | c1_1(V)) | c2_1(V)) | c0_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause182')).
% 0.60/0.80 tff(211,plain,
% 0.60/0.80 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[210, 209])).
% 0.60/0.80 tff(212,plain,
% 0.60/0.80 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[211, 207])).
% 0.60/0.80 tff(213,plain,(
% 0.60/0.80 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))),
% 0.60/0.80 inference(skolemize,[status(sab)],[212])).
% 0.60/0.80 tff(214,plain,
% 0.60/0.80 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[213, 206])).
% 0.60/0.80 tff(215,plain,
% 0.60/0.80 (^[U: $i] : refl((hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))))),
% 0.60/0.80 inference(bind,[status(th)],[])).
% 0.60/0.80 tff(216,plain,
% 0.60/0.80 (![U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.60/0.80 inference(quant_intro,[status(thm)],[215])).
% 0.60/0.80 tff(217,plain,
% 0.60/0.80 (![U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(218,plain,
% 0.60/0.80 (^[U: $i] : trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c0_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp12) <=> (((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp12))), rewrite((((~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U))) | hskp12) <=> (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp12) <=> (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))))),
% 0.60/0.80 inference(bind,[status(th)],[])).
% 0.60/0.80 tff(219,plain,
% 0.60/0.80 (![U: $i] : (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp12) <=> ![U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.60/0.80 inference(quant_intro,[status(thm)],[218])).
% 0.60/0.80 tff(220,axiom,(![U: $i] : (((((~c0_1(U)) | (~c1_1(U))) | (~ndr1_0)) | c3_1(U)) | hskp12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause148')).
% 0.60/0.80 tff(221,plain,
% 0.60/0.80 (![U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[220, 219])).
% 0.60/0.80 tff(222,plain,
% 0.60/0.80 (![U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[221, 217])).
% 0.60/0.80 tff(223,plain,(
% 0.60/0.80 ![U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.60/0.80 inference(skolemize,[status(sab)],[222])).
% 0.60/0.80 tff(224,plain,
% 0.60/0.80 (![U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[223, 216])).
% 0.60/0.80 tff(225,plain,
% 0.60/0.80 (((~hskp16) | c0_1(a151)) <=> ((~hskp16) | c0_1(a151))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(226,axiom,((~hskp16) | c0_1(a151)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause61')).
% 0.60/0.80 tff(227,plain,
% 0.60/0.80 ((~hskp16) | c0_1(a151)),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[226, 225])).
% 0.60/0.80 tff(228,plain,
% 0.60/0.80 ((~hskp16) | c0_1(a151)),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[227, 225])).
% 0.60/0.80 tff(229,plain,
% 0.60/0.80 ((~hskp16) | c0_1(a151)),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[228, 225])).
% 0.60/0.80 tff(230,plain,
% 0.60/0.80 ((~hskp16) | c0_1(a151)),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[229, 225])).
% 0.60/0.80 tff(231,plain,
% 0.60/0.80 ((~hskp16) | c0_1(a151)),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[230, 225])).
% 0.60/0.80 tff(232,plain,
% 0.60/0.80 (c0_1(a151)),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[231, 183])).
% 0.60/0.80 tff(233,plain,
% 0.60/0.80 (((~![U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp15 | c2_1(a151) | (~ndr1_0) | (~c1_1(a151)) | (~c0_1(a151)))) <=> ((~![U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp15 | c2_1(a151) | (~ndr1_0) | (~c1_1(a151)) | (~c0_1(a151)))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(234,plain,
% 0.60/0.80 ((hskp15 | (~ndr1_0) | c2_1(a151) | (~c1_1(a151)) | (~c0_1(a151))) <=> (hskp15 | c2_1(a151) | (~ndr1_0) | (~c1_1(a151)) | (~c0_1(a151)))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(235,plain,
% 0.60/0.80 (((~![U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp15 | (~ndr1_0) | c2_1(a151) | (~c1_1(a151)) | (~c0_1(a151)))) <=> ((~![U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp15 | c2_1(a151) | (~ndr1_0) | (~c1_1(a151)) | (~c0_1(a151))))),
% 0.60/0.80 inference(monotonicity,[status(thm)],[234])).
% 0.60/0.80 tff(236,plain,
% 0.60/0.80 (((~![U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp15 | (~ndr1_0) | c2_1(a151) | (~c1_1(a151)) | (~c0_1(a151)))) <=> ((~![U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp15 | c2_1(a151) | (~ndr1_0) | (~c1_1(a151)) | (~c0_1(a151)))),
% 0.60/0.80 inference(transitivity,[status(thm)],[235, 233])).
% 0.60/0.80 tff(237,plain,
% 0.60/0.80 ((~![U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp15 | (~ndr1_0) | c2_1(a151) | (~c1_1(a151)) | (~c0_1(a151)))),
% 0.60/0.80 inference(quant_inst,[status(thm)],[])).
% 0.60/0.80 tff(238,plain,
% 0.60/0.80 ((~![U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp15 | c2_1(a151) | (~ndr1_0) | (~c1_1(a151)) | (~c0_1(a151))),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[237, 236])).
% 0.60/0.80 tff(239,plain,
% 0.60/0.80 (hskp15),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[238, 175, 232, 197, 189, 63])).
% 0.60/0.80 tff(240,plain,
% 0.60/0.80 (((~hskp15) | c3_1(a149)) <=> ((~hskp15) | c3_1(a149))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(241,axiom,((~hskp15) | c3_1(a149)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause63')).
% 0.60/0.80 tff(242,plain,
% 0.60/0.80 ((~hskp15) | c3_1(a149)),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[241, 240])).
% 0.60/0.80 tff(243,plain,
% 0.60/0.80 ((~hskp15) | c3_1(a149)),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[242, 240])).
% 0.60/0.80 tff(244,plain,
% 0.60/0.80 ((~hskp15) | c3_1(a149)),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[243, 240])).
% 0.60/0.80 tff(245,plain,
% 0.60/0.80 ((~hskp15) | c3_1(a149)),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[244, 240])).
% 0.60/0.80 tff(246,plain,
% 0.60/0.80 ((~hskp15) | c3_1(a149)),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[245, 240])).
% 0.60/0.80 tff(247,plain,
% 0.60/0.80 (c3_1(a149)),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[246, 239])).
% 0.60/0.80 tff(248,assumption,(~c3_1(a128)), introduced(assumption)).
% 0.60/0.80 tff(249,plain,
% 0.60/0.80 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W)))),
% 0.60/0.80 inference(bind,[status(th)],[])).
% 0.60/0.80 tff(250,plain,
% 0.60/0.80 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.60/0.80 inference(quant_intro,[status(thm)],[249])).
% 0.60/0.80 tff(251,plain,
% 0.60/0.80 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(252,plain,
% 0.60/0.80 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)) | c0_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c0_1(W))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c0_1(W)))), ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c0_1(W)) | c1_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c1_1(W) | c0_1(W))), ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c1_1(W) | c0_1(W)))), (((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c1_1(W) | c0_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c1_1(W) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))), (((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))))),
% 0.60/0.80 inference(bind,[status(th)],[])).
% 0.60/0.80 tff(253,plain,
% 0.60/0.80 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.60/0.80 inference(quant_intro,[status(thm)],[252])).
% 0.60/0.80 tff(254,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause178')).
% 0.60/0.80 tff(255,plain,
% 0.60/0.80 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[254, 253])).
% 0.60/0.80 tff(256,plain,
% 0.60/0.80 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[255, 251])).
% 0.60/0.80 tff(257,plain,(
% 0.60/0.80 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.60/0.80 inference(skolemize,[status(sab)],[256])).
% 0.60/0.80 tff(258,plain,
% 0.60/0.80 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[257, 250])).
% 0.60/0.80 tff(259,assumption,(~c2_1(a128)), introduced(assumption)).
% 0.60/0.80 tff(260,plain,
% 0.60/0.80 (^[V: $i, U: $i] : refl((hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V))) <=> (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V))))),
% 0.60/0.80 inference(bind,[status(th)],[])).
% 0.60/0.80 tff(261,plain,
% 0.60/0.80 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.60/0.80 inference(quant_intro,[status(thm)],[260])).
% 0.60/0.80 tff(262,plain,
% 0.60/0.80 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(263,plain,
% 0.60/0.80 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c2_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c2_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c2_1(V) | (~c0_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | hskp17) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V))) | hskp17))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V))) | hskp17) <=> (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | hskp17) <=> (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))))),
% 0.60/0.80 inference(bind,[status(th)],[])).
% 0.60/0.80 tff(264,plain,
% 0.60/0.80 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | hskp17) <=> ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.60/0.80 inference(quant_intro,[status(thm)],[263])).
% 0.60/0.80 tff(265,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c2_1(U)) | c2_1(V)) | c3_1(V)) | hskp17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause170')).
% 0.60/0.80 tff(266,plain,
% 0.60/0.80 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[265, 264])).
% 0.60/0.80 tff(267,plain,
% 0.60/0.80 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[266, 262])).
% 0.60/0.80 tff(268,plain,(
% 0.60/0.80 ![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.60/0.80 inference(skolemize,[status(sab)],[267])).
% 0.60/0.80 tff(269,plain,
% 0.60/0.80 (![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[268, 261])).
% 0.60/0.80 tff(270,assumption,(~c0_1(a128)), introduced(assumption)).
% 0.60/0.80 tff(271,plain,
% 0.60/0.80 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a138) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | c1_1(a128) | (~c3_1(a138)) | (~c0_1(a138)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a138) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | c1_1(a128) | (~c3_1(a138)) | (~c0_1(a138)))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(272,plain,
% 0.60/0.80 (((~ndr1_0) | c1_1(a138) | (~c3_1(a138)) | (~c0_1(a138)) | c3_1(a128) | c0_1(a128) | c2_1(a128) | c2_1(a128) | c1_1(a128) | c0_1(a128)) <=> (c1_1(a138) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | c1_1(a128) | (~c3_1(a138)) | (~c0_1(a138)))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(273,plain,
% 0.60/0.80 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a138) | (~c3_1(a138)) | (~c0_1(a138)) | c3_1(a128) | c0_1(a128) | c2_1(a128) | c2_1(a128) | c1_1(a128) | c0_1(a128))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a138) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | c1_1(a128) | (~c3_1(a138)) | (~c0_1(a138))))),
% 0.60/0.80 inference(monotonicity,[status(thm)],[272])).
% 0.60/0.80 tff(274,plain,
% 0.60/0.80 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a138) | (~c3_1(a138)) | (~c0_1(a138)) | c3_1(a128) | c0_1(a128) | c2_1(a128) | c2_1(a128) | c1_1(a128) | c0_1(a128))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a138) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | c1_1(a128) | (~c3_1(a138)) | (~c0_1(a138)))),
% 0.60/0.80 inference(transitivity,[status(thm)],[273, 271])).
% 0.60/0.80 tff(275,plain,
% 0.60/0.80 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a138) | (~c3_1(a138)) | (~c0_1(a138)) | c3_1(a128) | c0_1(a128) | c2_1(a128) | c2_1(a128) | c1_1(a128) | c0_1(a128))),
% 0.60/0.80 inference(quant_inst,[status(thm)],[])).
% 0.60/0.80 tff(276,plain,
% 0.60/0.80 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a138) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | c1_1(a128) | (~c3_1(a138)) | (~c0_1(a138))),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[275, 274])).
% 0.60/0.80 tff(277,plain,
% 0.60/0.80 (c0_1(a128) | c1_1(a128)),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[276, 175, 141, 140, 139, 259, 248, 258])).
% 0.60/0.80 tff(278,plain,
% 0.60/0.80 (c1_1(a128)),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[277, 270])).
% 0.60/0.80 tff(279,plain,
% 0.60/0.80 (((~![U: $i] : (hskp21 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp21 | hskp18 | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c1_1(a128)))) <=> ((~![U: $i] : (hskp21 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | hskp21 | hskp18 | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c1_1(a128)))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(280,plain,
% 0.60/0.80 ((hskp21 | hskp18 | (~ndr1_0) | c3_1(a128) | c2_1(a128) | (~c1_1(a128))) <=> (hskp21 | hskp18 | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c1_1(a128)))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(281,plain,
% 0.60/0.80 (((~![U: $i] : (hskp21 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp21 | hskp18 | (~ndr1_0) | c3_1(a128) | c2_1(a128) | (~c1_1(a128)))) <=> ((~![U: $i] : (hskp21 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp21 | hskp18 | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c1_1(a128))))),
% 0.60/0.80 inference(monotonicity,[status(thm)],[280])).
% 0.60/0.80 tff(282,plain,
% 0.60/0.80 (((~![U: $i] : (hskp21 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp21 | hskp18 | (~ndr1_0) | c3_1(a128) | c2_1(a128) | (~c1_1(a128)))) <=> ((~![U: $i] : (hskp21 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | hskp21 | hskp18 | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c1_1(a128)))),
% 0.60/0.80 inference(transitivity,[status(thm)],[281, 279])).
% 0.60/0.80 tff(283,plain,
% 0.60/0.80 ((~![U: $i] : (hskp21 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp21 | hskp18 | (~ndr1_0) | c3_1(a128) | c2_1(a128) | (~c1_1(a128)))),
% 0.60/0.80 inference(quant_inst,[status(thm)],[])).
% 0.60/0.80 tff(284,plain,
% 0.60/0.80 ((~![U: $i] : (hskp21 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | hskp21 | hskp18 | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c1_1(a128))),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[283, 282])).
% 0.60/0.80 tff(285,plain,
% 0.60/0.80 (hskp21 | c2_1(a128) | (~c1_1(a128))),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[284, 175, 95, 248, 128])).
% 0.60/0.80 tff(286,plain,
% 0.60/0.80 (hskp21),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[285, 278, 259])).
% 0.60/0.80 tff(287,plain,
% 0.60/0.80 (((~hskp21) | (~c2_1(a170))) <=> ((~hskp21) | (~c2_1(a170)))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(288,plain,
% 0.60/0.80 (((~c2_1(a170)) | (~hskp21)) <=> ((~hskp21) | (~c2_1(a170)))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(289,axiom,((~c2_1(a170)) | (~hskp21)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause94')).
% 0.60/0.80 tff(290,plain,
% 0.60/0.80 ((~hskp21) | (~c2_1(a170))),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[289, 288])).
% 0.60/0.80 tff(291,plain,
% 0.60/0.80 ((~hskp21) | (~c2_1(a170))),
% 0.60/0.80 inference(modus_ponens,[status(thm)],[290, 287])).
% 0.60/0.80 tff(292,plain,
% 0.60/0.80 (~c2_1(a170)),
% 0.60/0.80 inference(unit_resolution,[status(thm)],[291, 286])).
% 0.60/0.80 tff(293,plain,
% 0.60/0.80 (((~hskp21) | (~c0_1(a170))) <=> ((~hskp21) | (~c0_1(a170)))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.80 tff(294,plain,
% 0.60/0.80 (((~c0_1(a170)) | (~hskp21)) <=> ((~hskp21) | (~c0_1(a170)))),
% 0.60/0.80 inference(rewrite,[status(thm)],[])).
% 0.60/0.81 tff(295,axiom,((~c0_1(a170)) | (~hskp21)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause93')).
% 0.60/0.81 tff(296,plain,
% 0.60/0.81 ((~hskp21) | (~c0_1(a170))),
% 0.60/0.81 inference(modus_ponens,[status(thm)],[295, 294])).
% 0.60/0.81 tff(297,plain,
% 0.60/0.81 ((~hskp21) | (~c0_1(a170))),
% 0.60/0.81 inference(modus_ponens,[status(thm)],[296, 293])).
% 0.60/0.81 tff(298,plain,
% 0.60/0.81 (~c0_1(a170)),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[297, 286])).
% 0.60/0.81 tff(299,plain,
% 0.60/0.81 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a170) | c2_1(a170) | c1_1(a138) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c3_1(a138)) | (~c0_1(a138)) | c1_1(a170))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a170) | c2_1(a170) | c1_1(a138) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c3_1(a138)) | (~c0_1(a138)) | c1_1(a170))),
% 0.60/0.81 inference(rewrite,[status(thm)],[])).
% 0.60/0.81 tff(300,plain,
% 0.60/0.81 (((~ndr1_0) | c1_1(a138) | (~c3_1(a138)) | (~c0_1(a138)) | c3_1(a128) | c0_1(a128) | c2_1(a128) | c2_1(a170) | c1_1(a170) | c0_1(a170)) <=> (c0_1(a170) | c2_1(a170) | c1_1(a138) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c3_1(a138)) | (~c0_1(a138)) | c1_1(a170))),
% 0.60/0.81 inference(rewrite,[status(thm)],[])).
% 0.60/0.81 tff(301,plain,
% 0.60/0.81 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a138) | (~c3_1(a138)) | (~c0_1(a138)) | c3_1(a128) | c0_1(a128) | c2_1(a128) | c2_1(a170) | c1_1(a170) | c0_1(a170))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a170) | c2_1(a170) | c1_1(a138) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c3_1(a138)) | (~c0_1(a138)) | c1_1(a170)))),
% 0.60/0.81 inference(monotonicity,[status(thm)],[300])).
% 0.60/0.81 tff(302,plain,
% 0.60/0.81 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a138) | (~c3_1(a138)) | (~c0_1(a138)) | c3_1(a128) | c0_1(a128) | c2_1(a128) | c2_1(a170) | c1_1(a170) | c0_1(a170))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a170) | c2_1(a170) | c1_1(a138) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c3_1(a138)) | (~c0_1(a138)) | c1_1(a170))),
% 0.60/0.81 inference(transitivity,[status(thm)],[301, 299])).
% 0.60/0.81 tff(303,plain,
% 0.60/0.81 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a138) | (~c3_1(a138)) | (~c0_1(a138)) | c3_1(a128) | c0_1(a128) | c2_1(a128) | c2_1(a170) | c1_1(a170) | c0_1(a170))),
% 0.60/0.81 inference(quant_inst,[status(thm)],[])).
% 0.60/0.81 tff(304,plain,
% 0.60/0.81 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a170) | c2_1(a170) | c1_1(a138) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c3_1(a138)) | (~c0_1(a138)) | c1_1(a170)),
% 0.60/0.81 inference(modus_ponens,[status(thm)],[303, 302])).
% 0.60/0.81 tff(305,plain,
% 0.60/0.81 (c1_1(a170)),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[304, 175, 141, 140, 298, 292, 139, 270, 259, 248, 258])).
% 0.60/0.81 tff(306,plain,
% 0.60/0.81 (^[V: $i, U: $i] : refl((hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) <=> (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))))),
% 0.60/0.81 inference(bind,[status(th)],[])).
% 0.60/0.81 tff(307,plain,
% 0.60/0.81 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.60/0.81 inference(quant_intro,[status(thm)],[306])).
% 0.60/0.81 tff(308,plain,
% 0.60/0.81 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.60/0.81 inference(rewrite,[status(thm)],[])).
% 0.60/0.81 tff(309,plain,
% 0.60/0.81 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V))))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c0_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c1_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c0_1(V)) | c3_1(V)) | hskp6) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) | hskp6))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V))) | hskp6) <=> (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c0_1(V)) | c3_1(V)) | hskp6) <=> (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))))),
% 0.60/0.81 inference(bind,[status(th)],[])).
% 0.60/0.81 tff(310,plain,
% 0.60/0.81 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c0_1(V)) | c3_1(V)) | hskp6) <=> ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.60/0.81 inference(quant_intro,[status(thm)],[309])).
% 0.60/0.81 tff(311,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | c0_1(U)) | c0_1(V)) | c3_1(V)) | hskp6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause165')).
% 0.60/0.81 tff(312,plain,
% 0.60/0.81 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.60/0.81 inference(modus_ponens,[status(thm)],[311, 310])).
% 0.60/0.81 tff(313,plain,
% 0.60/0.81 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.60/0.81 inference(modus_ponens,[status(thm)],[312, 308])).
% 0.60/0.81 tff(314,plain,(
% 0.60/0.81 ![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.60/0.81 inference(skolemize,[status(sab)],[313])).
% 0.60/0.81 tff(315,plain,
% 0.60/0.81 (![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))),
% 0.60/0.81 inference(modus_ponens,[status(thm)],[314, 307])).
% 0.60/0.81 tff(316,plain,
% 0.60/0.81 (((~hskp21) | c3_1(a170)) <=> ((~hskp21) | c3_1(a170))),
% 0.60/0.81 inference(rewrite,[status(thm)],[])).
% 0.60/0.81 tff(317,axiom,((~hskp21) | c3_1(a170)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause55')).
% 0.60/0.81 tff(318,plain,
% 0.60/0.81 ((~hskp21) | c3_1(a170)),
% 0.60/0.81 inference(modus_ponens,[status(thm)],[317, 316])).
% 0.60/0.81 tff(319,plain,
% 0.60/0.81 ((~hskp21) | c3_1(a170)),
% 0.60/0.81 inference(modus_ponens,[status(thm)],[318, 316])).
% 0.60/0.81 tff(320,plain,
% 0.60/0.81 ((~hskp21) | c3_1(a170)),
% 0.60/0.81 inference(modus_ponens,[status(thm)],[319, 316])).
% 0.60/0.81 tff(321,plain,
% 0.60/0.81 ((~hskp21) | c3_1(a170)),
% 0.60/0.81 inference(modus_ponens,[status(thm)],[320, 316])).
% 0.60/0.81 tff(322,plain,
% 0.60/0.81 ((~hskp21) | c3_1(a170)),
% 0.60/0.81 inference(modus_ponens,[status(thm)],[321, 316])).
% 0.60/0.81 tff(323,plain,
% 0.60/0.81 (c3_1(a170)),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[322, 286])).
% 0.60/0.81 tff(324,plain,
% 0.60/0.81 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | c0_1(a170) | c0_1(a128) | c3_1(a128) | (~ndr1_0) | (~c1_1(a128)) | (~c3_1(a170)) | (~c1_1(a170)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp6 | c0_1(a170) | c0_1(a128) | c3_1(a128) | (~ndr1_0) | (~c1_1(a128)) | (~c3_1(a170)) | (~c1_1(a170)))),
% 0.60/0.81 inference(rewrite,[status(thm)],[])).
% 0.60/0.81 tff(325,plain,
% 0.60/0.81 ((hskp6 | (~ndr1_0) | c0_1(a170) | (~c3_1(a170)) | (~c1_1(a170)) | c3_1(a128) | c0_1(a128) | (~c1_1(a128))) <=> (hskp6 | c0_1(a170) | c0_1(a128) | c3_1(a128) | (~ndr1_0) | (~c1_1(a128)) | (~c3_1(a170)) | (~c1_1(a170)))),
% 0.60/0.81 inference(rewrite,[status(thm)],[])).
% 0.60/0.81 tff(326,plain,
% 0.60/0.81 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | (~ndr1_0) | c0_1(a170) | (~c3_1(a170)) | (~c1_1(a170)) | c3_1(a128) | c0_1(a128) | (~c1_1(a128)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | c0_1(a170) | c0_1(a128) | c3_1(a128) | (~ndr1_0) | (~c1_1(a128)) | (~c3_1(a170)) | (~c1_1(a170))))),
% 0.60/0.81 inference(monotonicity,[status(thm)],[325])).
% 0.60/0.81 tff(327,plain,
% 0.60/0.81 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | (~ndr1_0) | c0_1(a170) | (~c3_1(a170)) | (~c1_1(a170)) | c3_1(a128) | c0_1(a128) | (~c1_1(a128)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp6 | c0_1(a170) | c0_1(a128) | c3_1(a128) | (~ndr1_0) | (~c1_1(a128)) | (~c3_1(a170)) | (~c1_1(a170)))),
% 0.60/0.81 inference(transitivity,[status(thm)],[326, 324])).
% 0.60/0.81 tff(328,plain,
% 0.60/0.81 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | (~ndr1_0) | c0_1(a170) | (~c3_1(a170)) | (~c1_1(a170)) | c3_1(a128) | c0_1(a128) | (~c1_1(a128)))),
% 0.60/0.81 inference(quant_inst,[status(thm)],[])).
% 0.60/0.81 tff(329,plain,
% 0.60/0.81 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp6 | c0_1(a170) | c0_1(a128) | c3_1(a128) | (~ndr1_0) | (~c1_1(a128)) | (~c3_1(a170)) | (~c1_1(a170))),
% 0.60/0.81 inference(modus_ponens,[status(thm)],[328, 327])).
% 0.60/0.81 tff(330,plain,
% 0.60/0.81 (hskp6 | (~c1_1(a170))),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[329, 175, 323, 298, 270, 248, 315, 278])).
% 0.60/0.81 tff(331,plain,
% 0.60/0.81 (hskp6),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[330, 305])).
% 0.60/0.81 tff(332,plain,
% 0.60/0.81 (((~hskp6) | (~c2_1(a133))) <=> ((~hskp6) | (~c2_1(a133)))),
% 0.60/0.81 inference(rewrite,[status(thm)],[])).
% 0.60/0.81 tff(333,plain,
% 0.60/0.81 (((~c2_1(a133)) | (~hskp6)) <=> ((~hskp6) | (~c2_1(a133)))),
% 0.60/0.81 inference(rewrite,[status(thm)],[])).
% 0.60/0.81 tff(334,axiom,((~c2_1(a133)) | (~hskp6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause120')).
% 0.60/0.81 tff(335,plain,
% 0.60/0.81 ((~hskp6) | (~c2_1(a133))),
% 0.60/0.81 inference(modus_ponens,[status(thm)],[334, 333])).
% 0.60/0.81 tff(336,plain,
% 0.60/0.81 ((~hskp6) | (~c2_1(a133))),
% 0.60/0.81 inference(modus_ponens,[status(thm)],[335, 332])).
% 0.60/0.81 tff(337,plain,
% 0.60/0.81 (~c2_1(a133)),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[336, 331])).
% 0.60/0.81 tff(338,plain,
% 0.60/0.81 (((~hskp6) | (~c1_1(a133))) <=> ((~hskp6) | (~c1_1(a133)))),
% 0.60/0.81 inference(rewrite,[status(thm)],[])).
% 0.60/0.81 tff(339,plain,
% 0.60/0.81 (((~c1_1(a133)) | (~hskp6)) <=> ((~hskp6) | (~c1_1(a133)))),
% 0.60/0.81 inference(rewrite,[status(thm)],[])).
% 0.60/0.81 tff(340,axiom,((~c1_1(a133)) | (~hskp6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause119')).
% 0.60/0.81 tff(341,plain,
% 0.60/0.81 ((~hskp6) | (~c1_1(a133))),
% 0.60/0.81 inference(modus_ponens,[status(thm)],[340, 339])).
% 0.60/0.81 tff(342,plain,
% 0.60/0.81 ((~hskp6) | (~c1_1(a133))),
% 0.60/0.81 inference(modus_ponens,[status(thm)],[341, 338])).
% 0.60/0.81 tff(343,plain,
% 0.60/0.81 (~c1_1(a133)),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[342, 331])).
% 0.60/0.81 tff(344,plain,
% 0.60/0.81 (((~hskp6) | (~c0_1(a133))) <=> ((~hskp6) | (~c0_1(a133)))),
% 0.60/0.81 inference(rewrite,[status(thm)],[])).
% 0.60/0.81 tff(345,plain,
% 0.60/0.81 (((~c0_1(a133)) | (~hskp6)) <=> ((~hskp6) | (~c0_1(a133)))),
% 0.60/0.81 inference(rewrite,[status(thm)],[])).
% 0.60/0.81 tff(346,axiom,((~c0_1(a133)) | (~hskp6)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause118')).
% 0.60/0.81 tff(347,plain,
% 0.60/0.81 ((~hskp6) | (~c0_1(a133))),
% 0.60/0.81 inference(modus_ponens,[status(thm)],[346, 345])).
% 0.60/0.81 tff(348,plain,
% 0.60/0.81 ((~hskp6) | (~c0_1(a133))),
% 0.60/0.81 inference(modus_ponens,[status(thm)],[347, 344])).
% 0.60/0.81 tff(349,plain,
% 0.60/0.81 (~c0_1(a133)),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[348, 331])).
% 0.60/0.81 tff(350,plain,
% 0.60/0.81 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a138) | c0_1(a133) | c1_1(a133) | c2_1(a133) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c3_1(a138)) | (~c0_1(a138)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a138) | c0_1(a133) | c1_1(a133) | c2_1(a133) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c3_1(a138)) | (~c0_1(a138)))),
% 0.60/0.81 inference(rewrite,[status(thm)],[])).
% 0.60/0.81 tff(351,plain,
% 0.60/0.81 (((~ndr1_0) | c1_1(a138) | (~c3_1(a138)) | (~c0_1(a138)) | c3_1(a128) | c0_1(a128) | c2_1(a128) | c2_1(a133) | c1_1(a133) | c0_1(a133)) <=> (c1_1(a138) | c0_1(a133) | c1_1(a133) | c2_1(a133) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c3_1(a138)) | (~c0_1(a138)))),
% 0.60/0.81 inference(rewrite,[status(thm)],[])).
% 0.60/0.81 tff(352,plain,
% 0.60/0.81 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a138) | (~c3_1(a138)) | (~c0_1(a138)) | c3_1(a128) | c0_1(a128) | c2_1(a128) | c2_1(a133) | c1_1(a133) | c0_1(a133))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a138) | c0_1(a133) | c1_1(a133) | c2_1(a133) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c3_1(a138)) | (~c0_1(a138))))),
% 0.60/0.81 inference(monotonicity,[status(thm)],[351])).
% 0.60/0.81 tff(353,plain,
% 0.60/0.81 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a138) | (~c3_1(a138)) | (~c0_1(a138)) | c3_1(a128) | c0_1(a128) | c2_1(a128) | c2_1(a133) | c1_1(a133) | c0_1(a133))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a138) | c0_1(a133) | c1_1(a133) | c2_1(a133) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c3_1(a138)) | (~c0_1(a138)))),
% 0.60/0.81 inference(transitivity,[status(thm)],[352, 350])).
% 0.60/0.81 tff(354,plain,
% 0.60/0.81 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a138) | (~c3_1(a138)) | (~c0_1(a138)) | c3_1(a128) | c0_1(a128) | c2_1(a128) | c2_1(a133) | c1_1(a133) | c0_1(a133))),
% 0.60/0.81 inference(quant_inst,[status(thm)],[])).
% 0.60/0.81 tff(355,plain,
% 0.60/0.81 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a138) | c0_1(a133) | c1_1(a133) | c2_1(a133) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c3_1(a138)) | (~c0_1(a138))),
% 0.60/0.81 inference(modus_ponens,[status(thm)],[354, 353])).
% 0.60/0.81 tff(356,plain,
% 0.60/0.81 ($false),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[355, 175, 141, 140, 139, 349, 343, 337, 270, 259, 248, 258])).
% 0.60/0.81 tff(357,plain,(c0_1(a128) | (~c0_1(a138)) | (~c3_1(a138)) | c1_1(a138) | c2_1(a128) | c3_1(a128) | hskp18), inference(lemma,lemma(discharge,[]))).
% 0.60/0.81 tff(358,plain,
% 0.60/0.81 (c0_1(a128)),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[357, 259, 140, 139, 141, 248, 95])).
% 0.60/0.81 tff(359,plain,
% 0.60/0.81 (~c1_1(a128)),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[285, 53, 259])).
% 0.60/0.81 tff(360,plain,
% 0.60/0.81 (^[V: $i, U: $i] : refl((hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))) <=> (hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))))),
% 0.60/0.81 inference(bind,[status(th)],[])).
% 0.60/0.81 tff(361,plain,
% 0.60/0.81 (![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.60/0.81 inference(quant_intro,[status(thm)],[360])).
% 0.60/0.81 tff(362,plain,
% 0.60/0.81 (![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.60/0.81 inference(rewrite,[status(thm)],[])).
% 0.60/0.81 tff(363,plain,
% 0.60/0.81 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) | c3_1(V)) | hskp19) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))) | hskp19))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V))) | hskp19) <=> (hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) | c3_1(V)) | hskp19) <=> (hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))))),
% 0.60/0.81 inference(bind,[status(th)],[])).
% 0.60/0.81 tff(364,plain,
% 0.60/0.81 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) | c3_1(V)) | hskp19) <=> ![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.60/0.81 inference(quant_intro,[status(thm)],[363])).
% 0.60/0.81 tff(365,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(U)) | c1_1(V)) | c3_1(V)) | hskp19)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause168')).
% 0.60/0.81 tff(366,plain,
% 0.60/0.81 (![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.60/0.81 inference(modus_ponens,[status(thm)],[365, 364])).
% 0.60/0.81 tff(367,plain,
% 0.60/0.81 (![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.60/0.81 inference(modus_ponens,[status(thm)],[366, 362])).
% 0.60/0.81 tff(368,plain,(
% 0.60/0.81 ![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.60/0.81 inference(skolemize,[status(sab)],[367])).
% 0.60/0.81 tff(369,plain,
% 0.60/0.81 (![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))),
% 0.60/0.81 inference(modus_ponens,[status(thm)],[368, 361])).
% 0.60/0.81 tff(370,plain,
% 0.60/0.81 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp19 | c1_1(a138) | (~c0_1(a128)) | c3_1(a128) | (~ndr1_0) | c1_1(a128) | (~c3_1(a138)) | (~c0_1(a138)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp19 | c1_1(a138) | (~c0_1(a128)) | c3_1(a128) | (~ndr1_0) | c1_1(a128) | (~c3_1(a138)) | (~c0_1(a138)))),
% 0.60/0.81 inference(rewrite,[status(thm)],[])).
% 0.60/0.81 tff(371,plain,
% 0.60/0.81 ((hskp19 | (~ndr1_0) | c1_1(a138) | (~c3_1(a138)) | (~c0_1(a138)) | c3_1(a128) | c1_1(a128) | (~c0_1(a128))) <=> (hskp19 | c1_1(a138) | (~c0_1(a128)) | c3_1(a128) | (~ndr1_0) | c1_1(a128) | (~c3_1(a138)) | (~c0_1(a138)))),
% 0.60/0.81 inference(rewrite,[status(thm)],[])).
% 0.60/0.81 tff(372,plain,
% 0.60/0.81 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp19 | (~ndr1_0) | c1_1(a138) | (~c3_1(a138)) | (~c0_1(a138)) | c3_1(a128) | c1_1(a128) | (~c0_1(a128)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp19 | c1_1(a138) | (~c0_1(a128)) | c3_1(a128) | (~ndr1_0) | c1_1(a128) | (~c3_1(a138)) | (~c0_1(a138))))),
% 0.60/0.81 inference(monotonicity,[status(thm)],[371])).
% 0.60/0.81 tff(373,plain,
% 0.60/0.81 (((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp19 | (~ndr1_0) | c1_1(a138) | (~c3_1(a138)) | (~c0_1(a138)) | c3_1(a128) | c1_1(a128) | (~c0_1(a128)))) <=> ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp19 | c1_1(a138) | (~c0_1(a128)) | c3_1(a128) | (~ndr1_0) | c1_1(a128) | (~c3_1(a138)) | (~c0_1(a138)))),
% 0.60/0.81 inference(transitivity,[status(thm)],[372, 370])).
% 0.60/0.81 tff(374,plain,
% 0.60/0.81 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | (hskp19 | (~ndr1_0) | c1_1(a138) | (~c3_1(a138)) | (~c0_1(a138)) | c3_1(a128) | c1_1(a128) | (~c0_1(a128)))),
% 0.60/0.81 inference(quant_inst,[status(thm)],[])).
% 0.60/0.81 tff(375,plain,
% 0.60/0.81 ((~![V: $i, U: $i] : (hskp19 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c0_1(V)))) | hskp19 | c1_1(a138) | (~c0_1(a128)) | c3_1(a128) | (~ndr1_0) | c1_1(a128) | (~c3_1(a138)) | (~c0_1(a138))),
% 0.60/0.81 inference(modus_ponens,[status(thm)],[374, 373])).
% 0.60/0.81 tff(376,plain,
% 0.60/0.81 (hskp19 | (~c0_1(a128)) | c1_1(a128)),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[375, 175, 141, 140, 139, 248, 369])).
% 0.60/0.81 tff(377,plain,
% 0.60/0.81 (hskp19),
% 0.60/0.81 inference(unit_resolution,[status(thm)],[376, 359, 358])).
% 0.60/0.81 tff(378,plain,
% 0.60/0.81 (((~hskp19) | (~c2_1(a162))) <=> ((~hskp19) | (~c2_1(a162)))),
% 0.60/0.81 inference(rewrite,[status(thm)],[])).
% 0.60/0.81 tff(379,plain,
% 0.60/0.81 (((~c2_1(a162)) | (~hskp19)) <=> ((~hskp19) | (~c2_1(a162)))),
% 0.60/0.82 inference(rewrite,[status(thm)],[])).
% 0.60/0.82 tff(380,axiom,((~c2_1(a162)) | (~hskp19)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause97')).
% 0.60/0.82 tff(381,plain,
% 0.60/0.82 ((~hskp19) | (~c2_1(a162))),
% 0.60/0.82 inference(modus_ponens,[status(thm)],[380, 379])).
% 0.60/0.82 tff(382,plain,
% 0.60/0.82 ((~hskp19) | (~c2_1(a162))),
% 0.60/0.82 inference(modus_ponens,[status(thm)],[381, 378])).
% 0.60/0.82 tff(383,plain,
% 0.60/0.82 (~c2_1(a162)),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[382, 377])).
% 0.60/0.82 tff(384,plain,
% 0.60/0.82 (((~hskp19) | c3_1(a162)) <=> ((~hskp19) | c3_1(a162))),
% 0.60/0.82 inference(rewrite,[status(thm)],[])).
% 0.60/0.82 tff(385,axiom,((~hskp19) | c3_1(a162)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause58')).
% 0.60/0.82 tff(386,plain,
% 0.60/0.82 ((~hskp19) | c3_1(a162)),
% 0.60/0.82 inference(modus_ponens,[status(thm)],[385, 384])).
% 0.60/0.82 tff(387,plain,
% 0.60/0.82 ((~hskp19) | c3_1(a162)),
% 0.60/0.82 inference(modus_ponens,[status(thm)],[386, 384])).
% 0.60/0.82 tff(388,plain,
% 0.60/0.82 ((~hskp19) | c3_1(a162)),
% 0.60/0.82 inference(modus_ponens,[status(thm)],[387, 384])).
% 0.60/0.82 tff(389,plain,
% 0.60/0.82 ((~hskp19) | c3_1(a162)),
% 0.60/0.82 inference(modus_ponens,[status(thm)],[388, 384])).
% 0.60/0.82 tff(390,plain,
% 0.60/0.82 ((~hskp19) | c3_1(a162)),
% 0.60/0.82 inference(modus_ponens,[status(thm)],[389, 384])).
% 0.60/0.82 tff(391,plain,
% 0.60/0.82 (c3_1(a162)),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[390, 377])).
% 0.60/0.82 tff(392,plain,
% 0.60/0.82 (((~hskp19) | c0_1(a162)) <=> ((~hskp19) | c0_1(a162))),
% 0.60/0.82 inference(rewrite,[status(thm)],[])).
% 0.60/0.82 tff(393,axiom,((~hskp19) | c0_1(a162)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause57')).
% 0.60/0.82 tff(394,plain,
% 0.60/0.82 ((~hskp19) | c0_1(a162)),
% 0.60/0.82 inference(modus_ponens,[status(thm)],[393, 392])).
% 0.60/0.82 tff(395,plain,
% 0.60/0.82 ((~hskp19) | c0_1(a162)),
% 0.60/0.82 inference(modus_ponens,[status(thm)],[394, 392])).
% 0.60/0.82 tff(396,plain,
% 0.60/0.82 ((~hskp19) | c0_1(a162)),
% 0.60/0.82 inference(modus_ponens,[status(thm)],[395, 392])).
% 0.60/0.82 tff(397,plain,
% 0.60/0.82 ((~hskp19) | c0_1(a162)),
% 0.60/0.82 inference(modus_ponens,[status(thm)],[396, 392])).
% 0.60/0.82 tff(398,plain,
% 0.60/0.82 ((~hskp19) | c0_1(a162)),
% 0.60/0.82 inference(modus_ponens,[status(thm)],[397, 392])).
% 0.60/0.82 tff(399,plain,
% 0.60/0.82 (c0_1(a162)),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[398, 377])).
% 0.60/0.82 tff(400,plain,
% 0.60/0.82 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp17 | c2_1(a162) | (~c0_1(a128)) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c3_1(a162)) | (~c0_1(a162)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp17 | c2_1(a162) | (~c0_1(a128)) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c3_1(a162)) | (~c0_1(a162)))),
% 0.60/0.82 inference(rewrite,[status(thm)],[])).
% 0.60/0.82 tff(401,plain,
% 0.60/0.82 ((hskp17 | (~ndr1_0) | c2_1(a162) | (~c3_1(a162)) | (~c0_1(a162)) | c3_1(a128) | c2_1(a128) | (~c0_1(a128))) <=> (hskp17 | c2_1(a162) | (~c0_1(a128)) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c3_1(a162)) | (~c0_1(a162)))),
% 0.60/0.82 inference(rewrite,[status(thm)],[])).
% 0.60/0.82 tff(402,plain,
% 0.60/0.82 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a162) | (~c3_1(a162)) | (~c0_1(a162)) | c3_1(a128) | c2_1(a128) | (~c0_1(a128)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp17 | c2_1(a162) | (~c0_1(a128)) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c3_1(a162)) | (~c0_1(a162))))),
% 0.60/0.82 inference(monotonicity,[status(thm)],[401])).
% 0.60/0.82 tff(403,plain,
% 0.60/0.82 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a162) | (~c3_1(a162)) | (~c0_1(a162)) | c3_1(a128) | c2_1(a128) | (~c0_1(a128)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp17 | c2_1(a162) | (~c0_1(a128)) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c3_1(a162)) | (~c0_1(a162)))),
% 0.60/0.82 inference(transitivity,[status(thm)],[402, 400])).
% 0.60/0.82 tff(404,plain,
% 0.60/0.82 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a162) | (~c3_1(a162)) | (~c0_1(a162)) | c3_1(a128) | c2_1(a128) | (~c0_1(a128)))),
% 0.60/0.82 inference(quant_inst,[status(thm)],[])).
% 0.60/0.82 tff(405,plain,
% 0.60/0.82 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp17 | c2_1(a162) | (~c0_1(a128)) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c3_1(a162)) | (~c0_1(a162))),
% 0.60/0.82 inference(modus_ponens,[status(thm)],[404, 403])).
% 0.60/0.82 tff(406,plain,
% 0.60/0.82 (hskp17),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[405, 175, 399, 391, 383, 358, 259, 248, 269])).
% 0.60/0.82 tff(407,plain,
% 0.60/0.82 (((~hskp17) | (~c3_1(a158))) <=> ((~hskp17) | (~c3_1(a158)))),
% 0.60/0.82 inference(rewrite,[status(thm)],[])).
% 0.60/0.82 tff(408,plain,
% 0.60/0.82 (((~c3_1(a158)) | (~hskp17)) <=> ((~hskp17) | (~c3_1(a158)))),
% 0.60/0.82 inference(rewrite,[status(thm)],[])).
% 0.60/0.82 tff(409,axiom,((~c3_1(a158)) | (~hskp17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause101')).
% 0.60/0.82 tff(410,plain,
% 0.60/0.82 ((~hskp17) | (~c3_1(a158))),
% 0.60/0.82 inference(modus_ponens,[status(thm)],[409, 408])).
% 0.60/0.82 tff(411,plain,
% 0.60/0.82 ((~hskp17) | (~c3_1(a158))),
% 0.60/0.82 inference(modus_ponens,[status(thm)],[410, 407])).
% 0.60/0.82 tff(412,plain,
% 0.60/0.82 (~c3_1(a158)),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[411, 406])).
% 0.60/0.82 tff(413,plain,
% 0.60/0.82 (((~hskp17) | (~c2_1(a158))) <=> ((~hskp17) | (~c2_1(a158)))),
% 0.60/0.82 inference(rewrite,[status(thm)],[])).
% 0.60/0.82 tff(414,plain,
% 0.60/0.82 (((~c2_1(a158)) | (~hskp17)) <=> ((~hskp17) | (~c2_1(a158)))),
% 0.60/0.82 inference(rewrite,[status(thm)],[])).
% 0.60/0.82 tff(415,axiom,((~c2_1(a158)) | (~hskp17)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause100')).
% 0.60/0.82 tff(416,plain,
% 0.60/0.82 ((~hskp17) | (~c2_1(a158))),
% 0.60/0.82 inference(modus_ponens,[status(thm)],[415, 414])).
% 0.60/0.82 tff(417,plain,
% 0.60/0.82 ((~hskp17) | (~c2_1(a158))),
% 0.60/0.82 inference(modus_ponens,[status(thm)],[416, 413])).
% 0.60/0.82 tff(418,plain,
% 0.60/0.82 (~c2_1(a158)),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[417, 406])).
% 0.60/0.82 tff(419,plain,
% 0.60/0.82 (((~hskp17) | c1_1(a158)) <=> ((~hskp17) | c1_1(a158))),
% 0.60/0.82 inference(rewrite,[status(thm)],[])).
% 0.60/0.82 tff(420,axiom,((~hskp17) | c1_1(a158)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause60')).
% 0.60/0.82 tff(421,plain,
% 0.60/0.82 ((~hskp17) | c1_1(a158)),
% 0.60/0.82 inference(modus_ponens,[status(thm)],[420, 419])).
% 0.60/0.82 tff(422,plain,
% 0.60/0.82 ((~hskp17) | c1_1(a158)),
% 0.60/0.82 inference(modus_ponens,[status(thm)],[421, 419])).
% 0.60/0.82 tff(423,plain,
% 0.60/0.82 ((~hskp17) | c1_1(a158)),
% 0.60/0.82 inference(modus_ponens,[status(thm)],[422, 419])).
% 0.60/0.82 tff(424,plain,
% 0.60/0.82 ((~hskp17) | c1_1(a158)),
% 0.60/0.82 inference(modus_ponens,[status(thm)],[423, 419])).
% 0.60/0.82 tff(425,plain,
% 0.60/0.82 ((~hskp17) | c1_1(a158)),
% 0.60/0.82 inference(modus_ponens,[status(thm)],[424, 419])).
% 0.60/0.82 tff(426,plain,
% 0.60/0.82 (c1_1(a158)),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[425, 406])).
% 0.60/0.82 tff(427,plain,
% 0.60/0.82 (((~![U: $i] : (hskp21 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp21 | hskp18 | c2_1(a158) | c3_1(a158) | (~ndr1_0) | (~c1_1(a158)))) <=> ((~![U: $i] : (hskp21 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | hskp21 | hskp18 | c2_1(a158) | c3_1(a158) | (~ndr1_0) | (~c1_1(a158)))),
% 0.60/0.82 inference(rewrite,[status(thm)],[])).
% 0.60/0.82 tff(428,plain,
% 0.60/0.82 ((hskp21 | hskp18 | (~ndr1_0) | c3_1(a158) | c2_1(a158) | (~c1_1(a158))) <=> (hskp21 | hskp18 | c2_1(a158) | c3_1(a158) | (~ndr1_0) | (~c1_1(a158)))),
% 0.60/0.82 inference(rewrite,[status(thm)],[])).
% 0.60/0.82 tff(429,plain,
% 0.60/0.82 (((~![U: $i] : (hskp21 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp21 | hskp18 | (~ndr1_0) | c3_1(a158) | c2_1(a158) | (~c1_1(a158)))) <=> ((~![U: $i] : (hskp21 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp21 | hskp18 | c2_1(a158) | c3_1(a158) | (~ndr1_0) | (~c1_1(a158))))),
% 0.60/0.82 inference(monotonicity,[status(thm)],[428])).
% 0.60/0.82 tff(430,plain,
% 0.60/0.82 (((~![U: $i] : (hskp21 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp21 | hskp18 | (~ndr1_0) | c3_1(a158) | c2_1(a158) | (~c1_1(a158)))) <=> ((~![U: $i] : (hskp21 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | hskp21 | hskp18 | c2_1(a158) | c3_1(a158) | (~ndr1_0) | (~c1_1(a158)))),
% 0.60/0.82 inference(transitivity,[status(thm)],[429, 427])).
% 0.60/0.82 tff(431,plain,
% 0.60/0.82 ((~![U: $i] : (hskp21 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp21 | hskp18 | (~ndr1_0) | c3_1(a158) | c2_1(a158) | (~c1_1(a158)))),
% 0.60/0.82 inference(quant_inst,[status(thm)],[])).
% 0.60/0.82 tff(432,plain,
% 0.60/0.82 ((~![U: $i] : (hskp21 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | hskp21 | hskp18 | c2_1(a158) | c3_1(a158) | (~ndr1_0) | (~c1_1(a158))),
% 0.60/0.82 inference(modus_ponens,[status(thm)],[431, 430])).
% 0.60/0.82 tff(433,plain,
% 0.60/0.82 ($false),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[432, 175, 53, 95, 426, 418, 412, 128])).
% 0.60/0.82 tff(434,plain,(hskp21 | hskp18 | c2_1(a128) | c3_1(a128) | (~c0_1(a138)) | (~c3_1(a138)) | c1_1(a138)), inference(lemma,lemma(discharge,[]))).
% 0.60/0.82 tff(435,plain,
% 0.60/0.82 (hskp21),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[434, 259, 95, 248, 141, 140, 139])).
% 0.60/0.82 tff(436,plain,
% 0.60/0.82 (~c0_1(a170)),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[297, 435])).
% 0.60/0.82 tff(437,plain,
% 0.60/0.82 (~c2_1(a170)),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[291, 435])).
% 0.60/0.82 tff(438,assumption,(~c2_1(a170)), introduced(assumption)).
% 0.60/0.82 tff(439,assumption,(~c0_1(a170)), introduced(assumption)).
% 0.60/0.82 tff(440,assumption,(~c3_1(a170)), introduced(assumption)).
% 0.60/0.82 tff(441,plain,
% 0.60/0.82 (~hskp21),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[322, 440])).
% 0.60/0.82 tff(442,plain,
% 0.60/0.82 (((~![U: $i] : (hskp21 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp21 | hskp18 | c3_1(a170) | c2_1(a170) | (~ndr1_0) | (~c1_1(a170)))) <=> ((~![U: $i] : (hskp21 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | hskp21 | hskp18 | c3_1(a170) | c2_1(a170) | (~ndr1_0) | (~c1_1(a170)))),
% 0.60/0.82 inference(rewrite,[status(thm)],[])).
% 0.60/0.82 tff(443,plain,
% 0.60/0.82 ((hskp21 | hskp18 | (~ndr1_0) | c3_1(a170) | c2_1(a170) | (~c1_1(a170))) <=> (hskp21 | hskp18 | c3_1(a170) | c2_1(a170) | (~ndr1_0) | (~c1_1(a170)))),
% 0.60/0.82 inference(rewrite,[status(thm)],[])).
% 0.60/0.82 tff(444,plain,
% 0.60/0.82 (((~![U: $i] : (hskp21 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp21 | hskp18 | (~ndr1_0) | c3_1(a170) | c2_1(a170) | (~c1_1(a170)))) <=> ((~![U: $i] : (hskp21 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp21 | hskp18 | c3_1(a170) | c2_1(a170) | (~ndr1_0) | (~c1_1(a170))))),
% 0.60/0.82 inference(monotonicity,[status(thm)],[443])).
% 0.60/0.82 tff(445,plain,
% 0.60/0.82 (((~![U: $i] : (hskp21 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp21 | hskp18 | (~ndr1_0) | c3_1(a170) | c2_1(a170) | (~c1_1(a170)))) <=> ((~![U: $i] : (hskp21 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | hskp21 | hskp18 | c3_1(a170) | c2_1(a170) | (~ndr1_0) | (~c1_1(a170)))),
% 0.60/0.82 inference(transitivity,[status(thm)],[444, 442])).
% 0.60/0.82 tff(446,plain,
% 0.60/0.82 ((~![U: $i] : (hskp21 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp21 | hskp18 | (~ndr1_0) | c3_1(a170) | c2_1(a170) | (~c1_1(a170)))),
% 0.60/0.82 inference(quant_inst,[status(thm)],[])).
% 0.60/0.82 tff(447,plain,
% 0.60/0.82 ((~![U: $i] : (hskp21 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | hskp21 | hskp18 | c3_1(a170) | c2_1(a170) | (~ndr1_0) | (~c1_1(a170))),
% 0.60/0.82 inference(modus_ponens,[status(thm)],[446, 445])).
% 0.60/0.82 tff(448,plain,
% 0.60/0.82 (hskp21 | c3_1(a170) | (~c1_1(a170))),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[447, 175, 95, 438, 128])).
% 0.60/0.82 tff(449,plain,
% 0.60/0.82 (~c1_1(a170)),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[448, 441, 440])).
% 0.60/0.82 tff(450,plain,
% 0.60/0.82 (~c1_1(a128)),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[285, 441, 259])).
% 0.60/0.82 tff(451,plain,
% 0.60/0.82 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W)))),
% 0.60/0.82 inference(bind,[status(th)],[])).
% 0.60/0.82 tff(452,plain,
% 0.60/0.82 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.60/0.82 inference(quant_intro,[status(thm)],[451])).
% 0.60/0.82 tff(453,plain,
% 0.60/0.82 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.60/0.82 inference(rewrite,[status(thm)],[])).
% 0.60/0.82 tff(454,plain,
% 0.60/0.82 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U))))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U))))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V)))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V)))), ((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c1_1(V) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))), ((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)))), (((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | c0_1(W)) <=> (((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) | c0_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c0_1(W))), (((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | c0_1(W)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c0_1(W)))), ((((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> (((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c0_1(W)) | c1_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c1_1(W) | c0_1(W))), ((((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c1_1(W) | c0_1(W)))), (((((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c1_1(W) | c0_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c1_1(W) | c0_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))), (((((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))))),
% 0.60/0.82 inference(bind,[status(th)],[])).
% 0.60/0.82 tff(455,plain,
% 0.60/0.82 (![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.60/0.82 inference(quant_intro,[status(thm)],[454])).
% 0.60/0.82 tff(456,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c2_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | c0_1(W)) | c1_1(W)) | c2_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause174')).
% 0.60/0.82 tff(457,plain,
% 0.60/0.82 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.60/0.82 inference(modus_ponens,[status(thm)],[456, 455])).
% 0.60/0.82 tff(458,plain,
% 0.60/0.82 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.60/0.82 inference(modus_ponens,[status(thm)],[457, 453])).
% 0.60/0.82 tff(459,plain,(
% 0.60/0.82 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.60/0.82 inference(skolemize,[status(sab)],[458])).
% 0.60/0.82 tff(460,plain,
% 0.60/0.82 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))),
% 0.60/0.82 inference(modus_ponens,[status(thm)],[459, 452])).
% 0.60/0.82 tff(461,assumption,(c0_1(a128)), introduced(assumption)).
% 0.60/0.82 tff(462,plain,
% 0.60/0.82 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c3_1(a170) | c0_1(a170) | c2_1(a170) | (~c0_1(a128)) | c2_1(a128) | (~ndr1_0) | c1_1(a128) | c1_1(a170))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c3_1(a170) | c0_1(a170) | c2_1(a170) | (~c0_1(a128)) | c2_1(a128) | (~ndr1_0) | c1_1(a128) | c1_1(a170))),
% 0.60/0.82 inference(rewrite,[status(thm)],[])).
% 0.60/0.82 tff(463,plain,
% 0.60/0.82 (((~ndr1_0) | c1_1(a128) | c2_1(a128) | (~c0_1(a128)) | c3_1(a170) | c1_1(a170) | c0_1(a170) | c2_1(a170) | c1_1(a170) | c0_1(a170)) <=> (c3_1(a170) | c0_1(a170) | c2_1(a170) | (~c0_1(a128)) | c2_1(a128) | (~ndr1_0) | c1_1(a128) | c1_1(a170))),
% 0.60/0.82 inference(rewrite,[status(thm)],[])).
% 0.60/0.82 tff(464,plain,
% 0.60/0.82 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a128) | c2_1(a128) | (~c0_1(a128)) | c3_1(a170) | c1_1(a170) | c0_1(a170) | c2_1(a170) | c1_1(a170) | c0_1(a170))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c3_1(a170) | c0_1(a170) | c2_1(a170) | (~c0_1(a128)) | c2_1(a128) | (~ndr1_0) | c1_1(a128) | c1_1(a170)))),
% 0.60/0.82 inference(monotonicity,[status(thm)],[463])).
% 0.60/0.82 tff(465,plain,
% 0.60/0.82 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a128) | c2_1(a128) | (~c0_1(a128)) | c3_1(a170) | c1_1(a170) | c0_1(a170) | c2_1(a170) | c1_1(a170) | c0_1(a170))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c3_1(a170) | c0_1(a170) | c2_1(a170) | (~c0_1(a128)) | c2_1(a128) | (~ndr1_0) | c1_1(a128) | c1_1(a170))),
% 0.60/0.82 inference(transitivity,[status(thm)],[464, 462])).
% 0.60/0.82 tff(466,plain,
% 0.60/0.82 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a128) | c2_1(a128) | (~c0_1(a128)) | c3_1(a170) | c1_1(a170) | c0_1(a170) | c2_1(a170) | c1_1(a170) | c0_1(a170))),
% 0.60/0.82 inference(quant_inst,[status(thm)],[])).
% 0.60/0.82 tff(467,plain,
% 0.60/0.82 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c3_1(a170) | c0_1(a170) | c2_1(a170) | (~c0_1(a128)) | c2_1(a128) | (~ndr1_0) | c1_1(a128) | c1_1(a170)),
% 0.60/0.82 inference(modus_ponens,[status(thm)],[466, 465])).
% 0.60/0.82 tff(468,plain,
% 0.60/0.82 ($false),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[467, 175, 440, 439, 438, 461, 259, 460, 450, 449])).
% 0.60/0.82 tff(469,plain,(c3_1(a170) | c0_1(a170) | c2_1(a170) | (~c0_1(a128)) | c2_1(a128) | hskp18 | c3_1(a128)), inference(lemma,lemma(discharge,[]))).
% 0.60/0.82 tff(470,plain,
% 0.60/0.82 (c3_1(a170)),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[469, 438, 439, 358, 259, 95, 248])).
% 0.60/0.82 tff(471,plain,
% 0.60/0.82 (((~hskp3) | (~c0_1(a128))) <=> ((~hskp3) | (~c0_1(a128)))),
% 0.60/0.82 inference(rewrite,[status(thm)],[])).
% 0.60/0.82 tff(472,plain,
% 0.60/0.82 (((~c0_1(a128)) | (~hskp3)) <=> ((~hskp3) | (~c0_1(a128)))),
% 0.60/0.82 inference(rewrite,[status(thm)],[])).
% 0.60/0.82 tff(473,axiom,((~c0_1(a128)) | (~hskp3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause123')).
% 0.60/0.82 tff(474,plain,
% 0.60/0.82 ((~hskp3) | (~c0_1(a128))),
% 0.60/0.82 inference(modus_ponens,[status(thm)],[473, 472])).
% 0.60/0.82 tff(475,plain,
% 0.60/0.82 ((~hskp3) | (~c0_1(a128))),
% 0.60/0.82 inference(modus_ponens,[status(thm)],[474, 471])).
% 0.60/0.82 tff(476,plain,
% 0.60/0.82 (~hskp3),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[475, 358])).
% 0.60/0.82 tff(477,plain,
% 0.60/0.82 (((~![U: $i] : (hskp14 | hskp3 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp14 | hskp3 | c0_1(a170) | c2_1(a170) | (~ndr1_0) | (~c3_1(a170)))) <=> ((~![U: $i] : (hskp14 | hskp3 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | hskp14 | hskp3 | c0_1(a170) | c2_1(a170) | (~ndr1_0) | (~c3_1(a170)))),
% 0.60/0.82 inference(rewrite,[status(thm)],[])).
% 0.60/0.82 tff(478,plain,
% 0.60/0.82 ((hskp14 | hskp3 | (~ndr1_0) | c0_1(a170) | c2_1(a170) | (~c3_1(a170))) <=> (hskp14 | hskp3 | c0_1(a170) | c2_1(a170) | (~ndr1_0) | (~c3_1(a170)))),
% 0.60/0.82 inference(rewrite,[status(thm)],[])).
% 0.60/0.82 tff(479,plain,
% 0.60/0.82 (((~![U: $i] : (hskp14 | hskp3 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp14 | hskp3 | (~ndr1_0) | c0_1(a170) | c2_1(a170) | (~c3_1(a170)))) <=> ((~![U: $i] : (hskp14 | hskp3 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp14 | hskp3 | c0_1(a170) | c2_1(a170) | (~ndr1_0) | (~c3_1(a170))))),
% 0.60/0.82 inference(monotonicity,[status(thm)],[478])).
% 0.60/0.82 tff(480,plain,
% 0.60/0.82 (((~![U: $i] : (hskp14 | hskp3 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp14 | hskp3 | (~ndr1_0) | c0_1(a170) | c2_1(a170) | (~c3_1(a170)))) <=> ((~![U: $i] : (hskp14 | hskp3 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | hskp14 | hskp3 | c0_1(a170) | c2_1(a170) | (~ndr1_0) | (~c3_1(a170)))),
% 0.60/0.82 inference(transitivity,[status(thm)],[479, 477])).
% 0.60/0.82 tff(481,plain,
% 0.60/0.82 ((~![U: $i] : (hskp14 | hskp3 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp14 | hskp3 | (~ndr1_0) | c0_1(a170) | c2_1(a170) | (~c3_1(a170)))),
% 0.60/0.82 inference(quant_inst,[status(thm)],[])).
% 0.60/0.82 tff(482,plain,
% 0.60/0.82 ((~![U: $i] : (hskp14 | hskp3 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | hskp14 | hskp3 | c0_1(a170) | c2_1(a170) | (~ndr1_0) | (~c3_1(a170))),
% 0.60/0.82 inference(modus_ponens,[status(thm)],[481, 480])).
% 0.60/0.82 tff(483,plain,
% 0.60/0.82 (hskp14 | c2_1(a170) | (~c3_1(a170))),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[482, 175, 476, 439, 51])).
% 0.60/0.82 tff(484,plain,
% 0.60/0.82 (hskp14),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[483, 470, 438])).
% 0.60/0.82 tff(485,plain,
% 0.60/0.82 (((~hskp14) | (~c3_1(a145))) <=> ((~hskp14) | (~c3_1(a145)))),
% 0.60/0.82 inference(rewrite,[status(thm)],[])).
% 0.60/0.82 tff(486,plain,
% 0.60/0.82 (((~c3_1(a145)) | (~hskp14)) <=> ((~hskp14) | (~c3_1(a145)))),
% 0.60/0.82 inference(rewrite,[status(thm)],[])).
% 0.60/0.82 tff(487,axiom,((~c3_1(a145)) | (~hskp14)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause107')).
% 0.60/0.82 tff(488,plain,
% 0.60/0.82 ((~hskp14) | (~c3_1(a145))),
% 0.60/0.82 inference(modus_ponens,[status(thm)],[487, 486])).
% 0.60/0.82 tff(489,plain,
% 0.60/0.82 ((~hskp14) | (~c3_1(a145))),
% 0.60/0.82 inference(modus_ponens,[status(thm)],[488, 485])).
% 0.60/0.82 tff(490,plain,
% 0.60/0.82 (~c3_1(a145)),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[489, 484])).
% 0.60/0.82 tff(491,plain,
% 0.60/0.82 (((~hskp14) | (~c1_1(a145))) <=> ((~hskp14) | (~c1_1(a145)))),
% 0.60/0.82 inference(rewrite,[status(thm)],[])).
% 0.60/0.82 tff(492,plain,
% 0.60/0.82 (((~c1_1(a145)) | (~hskp14)) <=> ((~hskp14) | (~c1_1(a145)))),
% 0.60/0.82 inference(rewrite,[status(thm)],[])).
% 0.60/0.82 tff(493,axiom,((~c1_1(a145)) | (~hskp14)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause106')).
% 0.60/0.82 tff(494,plain,
% 0.60/0.82 ((~hskp14) | (~c1_1(a145))),
% 0.60/0.82 inference(modus_ponens,[status(thm)],[493, 492])).
% 0.60/0.82 tff(495,plain,
% 0.60/0.82 ((~hskp14) | (~c1_1(a145))),
% 0.60/0.82 inference(modus_ponens,[status(thm)],[494, 491])).
% 0.60/0.82 tff(496,plain,
% 0.60/0.82 (~c1_1(a145)),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[495, 484])).
% 0.60/0.82 tff(497,plain,
% 0.60/0.82 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp3 | c0_1(a170) | c2_1(a170) | c1_1(a145) | c3_1(a145) | (~ndr1_0) | (~c2_1(a145)) | (~c3_1(a170)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp3 | c0_1(a170) | c2_1(a170) | c1_1(a145) | c3_1(a145) | (~ndr1_0) | (~c2_1(a145)) | (~c3_1(a170)))),
% 0.60/0.82 inference(rewrite,[status(thm)],[])).
% 0.60/0.82 tff(498,plain,
% 0.60/0.82 ((hskp3 | (~ndr1_0) | c3_1(a145) | c1_1(a145) | (~c2_1(a145)) | c0_1(a170) | c2_1(a170) | (~c3_1(a170))) <=> (hskp3 | c0_1(a170) | c2_1(a170) | c1_1(a145) | c3_1(a145) | (~ndr1_0) | (~c2_1(a145)) | (~c3_1(a170)))),
% 0.60/0.82 inference(rewrite,[status(thm)],[])).
% 0.60/0.82 tff(499,plain,
% 0.60/0.82 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp3 | (~ndr1_0) | c3_1(a145) | c1_1(a145) | (~c2_1(a145)) | c0_1(a170) | c2_1(a170) | (~c3_1(a170)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp3 | c0_1(a170) | c2_1(a170) | c1_1(a145) | c3_1(a145) | (~ndr1_0) | (~c2_1(a145)) | (~c3_1(a170))))),
% 0.60/0.82 inference(monotonicity,[status(thm)],[498])).
% 0.60/0.82 tff(500,plain,
% 0.60/0.82 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp3 | (~ndr1_0) | c3_1(a145) | c1_1(a145) | (~c2_1(a145)) | c0_1(a170) | c2_1(a170) | (~c3_1(a170)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp3 | c0_1(a170) | c2_1(a170) | c1_1(a145) | c3_1(a145) | (~ndr1_0) | (~c2_1(a145)) | (~c3_1(a170)))),
% 0.60/0.82 inference(transitivity,[status(thm)],[499, 497])).
% 0.60/0.82 tff(501,plain,
% 0.60/0.82 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp3 | (~ndr1_0) | c3_1(a145) | c1_1(a145) | (~c2_1(a145)) | c0_1(a170) | c2_1(a170) | (~c3_1(a170)))),
% 0.60/0.82 inference(quant_inst,[status(thm)],[])).
% 0.60/0.82 tff(502,plain,
% 0.60/0.82 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp3 | c0_1(a170) | c2_1(a170) | c1_1(a145) | c3_1(a145) | (~ndr1_0) | (~c2_1(a145)) | (~c3_1(a170))),
% 0.60/0.82 inference(modus_ponens,[status(thm)],[501, 500])).
% 0.60/0.82 tff(503,plain,
% 0.60/0.82 (~c2_1(a145)),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[502, 175, 476, 470, 439, 438, 496, 490, 41])).
% 0.60/0.82 tff(504,plain,
% 0.60/0.82 (((~hskp14) | (~c0_1(a145))) <=> ((~hskp14) | (~c0_1(a145)))),
% 0.60/0.82 inference(rewrite,[status(thm)],[])).
% 0.60/0.82 tff(505,plain,
% 0.60/0.82 (((~c0_1(a145)) | (~hskp14)) <=> ((~hskp14) | (~c0_1(a145)))),
% 0.60/0.82 inference(rewrite,[status(thm)],[])).
% 0.60/0.82 tff(506,axiom,((~c0_1(a145)) | (~hskp14)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause105')).
% 0.60/0.82 tff(507,plain,
% 0.60/0.82 ((~hskp14) | (~c0_1(a145))),
% 0.60/0.82 inference(modus_ponens,[status(thm)],[506, 505])).
% 0.60/0.82 tff(508,plain,
% 0.60/0.82 ((~hskp14) | (~c0_1(a145))),
% 0.60/0.82 inference(modus_ponens,[status(thm)],[507, 504])).
% 0.60/0.82 tff(509,plain,
% 0.60/0.82 (~c0_1(a145)),
% 0.60/0.82 inference(unit_resolution,[status(thm)],[508, 484])).
% 0.60/0.82 tff(510,plain,
% 0.60/0.82 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a145) | c1_1(a145) | c3_1(a145) | c1_1(a138) | (~ndr1_0) | (~c3_1(a138)) | (~c0_1(a138)) | c2_1(a145))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a145) | c1_1(a145) | c3_1(a145) | c1_1(a138) | (~ndr1_0) | (~c3_1(a138)) | (~c0_1(a138)) | c2_1(a145))),
% 0.60/0.83 inference(rewrite,[status(thm)],[])).
% 0.60/0.83 tff(511,plain,
% 0.60/0.83 (((~ndr1_0) | c1_1(a138) | (~c3_1(a138)) | (~c0_1(a138)) | c3_1(a145) | c0_1(a145) | c2_1(a145) | c2_1(a145) | c1_1(a145) | c0_1(a145)) <=> (c0_1(a145) | c1_1(a145) | c3_1(a145) | c1_1(a138) | (~ndr1_0) | (~c3_1(a138)) | (~c0_1(a138)) | c2_1(a145))),
% 0.60/0.83 inference(rewrite,[status(thm)],[])).
% 0.60/0.83 tff(512,plain,
% 0.60/0.83 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a138) | (~c3_1(a138)) | (~c0_1(a138)) | c3_1(a145) | c0_1(a145) | c2_1(a145) | c2_1(a145) | c1_1(a145) | c0_1(a145))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a145) | c1_1(a145) | c3_1(a145) | c1_1(a138) | (~ndr1_0) | (~c3_1(a138)) | (~c0_1(a138)) | c2_1(a145)))),
% 0.60/0.83 inference(monotonicity,[status(thm)],[511])).
% 0.60/0.83 tff(513,plain,
% 0.60/0.83 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a138) | (~c3_1(a138)) | (~c0_1(a138)) | c3_1(a145) | c0_1(a145) | c2_1(a145) | c2_1(a145) | c1_1(a145) | c0_1(a145))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a145) | c1_1(a145) | c3_1(a145) | c1_1(a138) | (~ndr1_0) | (~c3_1(a138)) | (~c0_1(a138)) | c2_1(a145))),
% 0.60/0.83 inference(transitivity,[status(thm)],[512, 510])).
% 0.60/0.83 tff(514,plain,
% 0.60/0.83 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a138) | (~c3_1(a138)) | (~c0_1(a138)) | c3_1(a145) | c0_1(a145) | c2_1(a145) | c2_1(a145) | c1_1(a145) | c0_1(a145))),
% 0.60/0.83 inference(quant_inst,[status(thm)],[])).
% 0.60/0.83 tff(515,plain,
% 0.60/0.83 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a145) | c1_1(a145) | c3_1(a145) | c1_1(a138) | (~ndr1_0) | (~c3_1(a138)) | (~c0_1(a138)) | c2_1(a145)),
% 0.60/0.83 inference(modus_ponens,[status(thm)],[514, 513])).
% 0.60/0.83 tff(516,plain,
% 0.60/0.83 ($false),
% 0.60/0.83 inference(unit_resolution,[status(thm)],[515, 175, 141, 140, 509, 496, 490, 139, 258, 503])).
% 0.60/0.83 tff(517,plain,(c2_1(a170) | (~c0_1(a138)) | (~c3_1(a138)) | c1_1(a138) | c0_1(a170) | c2_1(a128) | hskp18 | c3_1(a128)), inference(lemma,lemma(discharge,[]))).
% 0.60/0.83 tff(518,plain,
% 0.60/0.83 ($false),
% 0.60/0.83 inference(unit_resolution,[status(thm)],[517, 437, 436, 140, 139, 141, 259, 95, 248])).
% 0.60/0.83 tff(519,plain,(c2_1(a128) | (~c3_1(a138)) | c1_1(a138) | (~c0_1(a138)) | hskp18 | c3_1(a128)), inference(lemma,lemma(discharge,[]))).
% 0.60/0.83 tff(520,plain,
% 0.60/0.83 (c2_1(a128)),
% 0.60/0.83 inference(unit_resolution,[status(thm)],[519, 248, 139, 141, 95, 140])).
% 0.60/0.83 tff(521,plain,
% 0.60/0.83 (((~hskp15) | (~c2_1(a149))) <=> ((~hskp15) | (~c2_1(a149)))),
% 0.60/0.83 inference(rewrite,[status(thm)],[])).
% 0.60/0.83 tff(522,plain,
% 0.60/0.83 (((~c2_1(a149)) | (~hskp15)) <=> ((~hskp15) | (~c2_1(a149)))),
% 0.60/0.83 inference(rewrite,[status(thm)],[])).
% 0.60/0.83 tff(523,axiom,((~c2_1(a149)) | (~hskp15)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause104')).
% 0.60/0.83 tff(524,plain,
% 0.60/0.83 ((~hskp15) | (~c2_1(a149))),
% 0.60/0.83 inference(modus_ponens,[status(thm)],[523, 522])).
% 0.60/0.83 tff(525,plain,
% 0.60/0.83 ((~hskp15) | (~c2_1(a149))),
% 0.60/0.83 inference(modus_ponens,[status(thm)],[524, 521])).
% 0.60/0.83 tff(526,plain,
% 0.60/0.83 (~c2_1(a149)),
% 0.60/0.83 inference(unit_resolution,[status(thm)],[525, 239])).
% 0.60/0.83 tff(527,plain,
% 0.60/0.83 (((~hskp15) | (~c1_1(a149))) <=> ((~hskp15) | (~c1_1(a149)))),
% 0.60/0.83 inference(rewrite,[status(thm)],[])).
% 0.60/0.83 tff(528,plain,
% 0.60/0.83 (((~c1_1(a149)) | (~hskp15)) <=> ((~hskp15) | (~c1_1(a149)))),
% 0.60/0.83 inference(rewrite,[status(thm)],[])).
% 0.60/0.83 tff(529,axiom,((~c1_1(a149)) | (~hskp15)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause103')).
% 0.60/0.83 tff(530,plain,
% 0.60/0.83 ((~hskp15) | (~c1_1(a149))),
% 0.60/0.83 inference(modus_ponens,[status(thm)],[529, 528])).
% 0.60/0.83 tff(531,plain,
% 0.60/0.83 ((~hskp15) | (~c1_1(a149))),
% 0.60/0.83 inference(modus_ponens,[status(thm)],[530, 527])).
% 0.60/0.83 tff(532,plain,
% 0.60/0.83 (~c1_1(a149)),
% 0.60/0.83 inference(unit_resolution,[status(thm)],[531, 239])).
% 0.60/0.83 tff(533,assumption,(c3_1(a151)), introduced(assumption)).
% 0.60/0.83 tff(534,assumption,(~c1_1(a128)), introduced(assumption)).
% 0.60/0.83 tff(535,plain,
% 0.60/0.83 (^[U: $i] : refl((hskp3 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) <=> (hskp3 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))))),
% 0.60/0.83 inference(bind,[status(th)],[])).
% 0.60/0.83 tff(536,plain,
% 0.60/0.83 (![U: $i] : (hskp3 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp3 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.60/0.83 inference(quant_intro,[status(thm)],[535])).
% 0.60/0.83 tff(537,plain,
% 0.60/0.83 (![U: $i] : (hskp3 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) <=> ![U: $i] : (hskp3 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.60/0.83 inference(rewrite,[status(thm)],[])).
% 0.60/0.83 tff(538,plain,
% 0.60/0.83 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c2_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c2_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c2_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U)))), ((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c2_1(U))))), (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c2_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c2_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))), (((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp1) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp1))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp1) <=> (hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))), ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp1) <=> (hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp1) | hskp3) <=> ((hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp3))), rewrite(((hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U))) | hskp3) <=> (hskp3 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))), (((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp1) | hskp3) <=> (hskp3 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))))),
% 0.60/0.83 inference(bind,[status(th)],[])).
% 0.60/0.83 tff(539,plain,
% 0.60/0.83 (![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp1) | hskp3) <=> ![U: $i] : (hskp3 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.60/0.83 inference(quant_intro,[status(thm)],[538])).
% 0.60/0.83 tff(540,axiom,(![U: $i] : ((((((~c2_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | hskp1) | hskp3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause131')).
% 0.60/0.83 tff(541,plain,
% 0.60/0.83 (![U: $i] : (hskp3 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.60/0.83 inference(modus_ponens,[status(thm)],[540, 539])).
% 0.60/0.83 tff(542,plain,
% 0.60/0.83 (![U: $i] : (hskp3 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.60/0.83 inference(modus_ponens,[status(thm)],[541, 537])).
% 0.60/0.83 tff(543,plain,(
% 0.60/0.83 ![U: $i] : (hskp3 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.60/0.83 inference(skolemize,[status(sab)],[542])).
% 0.60/0.83 tff(544,plain,
% 0.60/0.83 (![U: $i] : (hskp3 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))),
% 0.60/0.83 inference(modus_ponens,[status(thm)],[543, 536])).
% 0.60/0.83 tff(545,assumption,(c2_1(a128)), introduced(assumption)).
% 0.60/0.83 tff(546,plain,
% 0.60/0.83 (((~hskp3) | (~c2_1(a128))) <=> ((~hskp3) | (~c2_1(a128)))),
% 0.60/0.83 inference(rewrite,[status(thm)],[])).
% 0.60/0.83 tff(547,plain,
% 0.60/0.83 (((~c2_1(a128)) | (~hskp3)) <=> ((~hskp3) | (~c2_1(a128)))),
% 0.60/0.83 inference(rewrite,[status(thm)],[])).
% 0.60/0.83 tff(548,axiom,((~c2_1(a128)) | (~hskp3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause124')).
% 0.60/0.83 tff(549,plain,
% 0.60/0.83 ((~hskp3) | (~c2_1(a128))),
% 0.60/0.83 inference(modus_ponens,[status(thm)],[548, 547])).
% 0.60/0.83 tff(550,plain,
% 0.60/0.83 ((~hskp3) | (~c2_1(a128))),
% 0.60/0.83 inference(modus_ponens,[status(thm)],[549, 546])).
% 0.60/0.83 tff(551,plain,
% 0.60/0.83 (~hskp3),
% 0.60/0.83 inference(unit_resolution,[status(thm)],[550, 545])).
% 0.60/0.83 tff(552,plain,
% 0.60/0.83 (((~![U: $i] : (hskp3 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp3 | hskp1 | c0_1(a128) | (~c2_1(a128)) | (~ndr1_0) | c1_1(a128))) <=> ((~![U: $i] : (hskp3 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp3 | hskp1 | c0_1(a128) | (~c2_1(a128)) | (~ndr1_0) | c1_1(a128))),
% 0.60/0.83 inference(rewrite,[status(thm)],[])).
% 0.60/0.83 tff(553,plain,
% 0.60/0.83 ((hskp3 | hskp1 | (~ndr1_0) | c1_1(a128) | c0_1(a128) | (~c2_1(a128))) <=> (hskp3 | hskp1 | c0_1(a128) | (~c2_1(a128)) | (~ndr1_0) | c1_1(a128))),
% 0.60/0.83 inference(rewrite,[status(thm)],[])).
% 0.60/0.83 tff(554,plain,
% 0.60/0.83 (((~![U: $i] : (hskp3 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp3 | hskp1 | (~ndr1_0) | c1_1(a128) | c0_1(a128) | (~c2_1(a128)))) <=> ((~![U: $i] : (hskp3 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp3 | hskp1 | c0_1(a128) | (~c2_1(a128)) | (~ndr1_0) | c1_1(a128)))),
% 0.60/0.83 inference(monotonicity,[status(thm)],[553])).
% 0.60/0.83 tff(555,plain,
% 0.60/0.83 (((~![U: $i] : (hskp3 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp3 | hskp1 | (~ndr1_0) | c1_1(a128) | c0_1(a128) | (~c2_1(a128)))) <=> ((~![U: $i] : (hskp3 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp3 | hskp1 | c0_1(a128) | (~c2_1(a128)) | (~ndr1_0) | c1_1(a128))),
% 0.60/0.83 inference(transitivity,[status(thm)],[554, 552])).
% 0.60/0.83 tff(556,plain,
% 0.60/0.83 ((~![U: $i] : (hskp3 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp3 | hskp1 | (~ndr1_0) | c1_1(a128) | c0_1(a128) | (~c2_1(a128)))),
% 0.60/0.83 inference(quant_inst,[status(thm)],[])).
% 0.60/0.83 tff(557,plain,
% 0.60/0.83 ((~![U: $i] : (hskp3 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp3 | hskp1 | c0_1(a128) | (~c2_1(a128)) | (~ndr1_0) | c1_1(a128)),
% 0.60/0.83 inference(modus_ponens,[status(thm)],[556, 555])).
% 0.60/0.83 tff(558,plain,
% 0.60/0.83 (hskp1 | c0_1(a128) | c1_1(a128)),
% 0.60/0.83 inference(unit_resolution,[status(thm)],[557, 175, 551, 545, 544])).
% 0.60/0.83 tff(559,plain,
% 0.60/0.83 (hskp1),
% 0.60/0.83 inference(unit_resolution,[status(thm)],[558, 534, 270])).
% 0.60/0.83 tff(560,plain,
% 0.60/0.83 (((~hskp1) | (~c3_1(a125))) <=> ((~hskp1) | (~c3_1(a125)))),
% 0.60/0.83 inference(rewrite,[status(thm)],[])).
% 0.60/0.83 tff(561,plain,
% 0.60/0.83 (((~c3_1(a125)) | (~hskp1)) <=> ((~hskp1) | (~c3_1(a125)))),
% 0.60/0.83 inference(rewrite,[status(thm)],[])).
% 0.60/0.83 tff(562,axiom,((~c3_1(a125)) | (~hskp1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause128')).
% 0.60/0.83 tff(563,plain,
% 0.60/0.83 ((~hskp1) | (~c3_1(a125))),
% 0.60/0.83 inference(modus_ponens,[status(thm)],[562, 561])).
% 0.60/0.83 tff(564,plain,
% 0.60/0.83 ((~hskp1) | (~c3_1(a125))),
% 0.60/0.83 inference(modus_ponens,[status(thm)],[563, 560])).
% 0.60/0.83 tff(565,plain,
% 0.60/0.83 (~c3_1(a125)),
% 0.60/0.83 inference(unit_resolution,[status(thm)],[564, 559])).
% 0.60/0.83 tff(566,plain,
% 0.60/0.83 (((~hskp1) | c1_1(a125)) <=> ((~hskp1) | c1_1(a125))),
% 0.60/0.83 inference(rewrite,[status(thm)],[])).
% 0.60/0.83 tff(567,axiom,((~hskp1) | c1_1(a125)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause81')).
% 0.60/0.83 tff(568,plain,
% 0.60/0.83 ((~hskp1) | c1_1(a125)),
% 0.60/0.83 inference(modus_ponens,[status(thm)],[567, 566])).
% 0.60/0.83 tff(569,plain,
% 0.60/0.83 ((~hskp1) | c1_1(a125)),
% 0.60/0.83 inference(modus_ponens,[status(thm)],[568, 566])).
% 0.60/0.83 tff(570,plain,
% 0.60/0.83 ((~hskp1) | c1_1(a125)),
% 0.60/0.83 inference(modus_ponens,[status(thm)],[569, 566])).
% 0.60/0.83 tff(571,plain,
% 0.60/0.83 ((~hskp1) | c1_1(a125)),
% 0.60/0.83 inference(modus_ponens,[status(thm)],[570, 566])).
% 0.60/0.83 tff(572,plain,
% 0.60/0.83 ((~hskp1) | c1_1(a125)),
% 0.60/0.83 inference(modus_ponens,[status(thm)],[571, 566])).
% 0.60/0.83 tff(573,plain,
% 0.60/0.83 (c1_1(a125)),
% 0.60/0.83 inference(unit_resolution,[status(thm)],[572, 559])).
% 0.60/0.83 tff(574,plain,
% 0.60/0.83 (((~hskp1) | c0_1(a125)) <=> ((~hskp1) | c0_1(a125))),
% 0.60/0.83 inference(rewrite,[status(thm)],[])).
% 0.60/0.83 tff(575,axiom,((~hskp1) | c0_1(a125)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause80')).
% 0.60/0.83 tff(576,plain,
% 0.60/0.83 ((~hskp1) | c0_1(a125)),
% 0.60/0.83 inference(modus_ponens,[status(thm)],[575, 574])).
% 0.60/0.83 tff(577,plain,
% 0.60/0.83 ((~hskp1) | c0_1(a125)),
% 0.60/0.83 inference(modus_ponens,[status(thm)],[576, 574])).
% 0.60/0.83 tff(578,plain,
% 0.60/0.83 ((~hskp1) | c0_1(a125)),
% 0.60/0.83 inference(modus_ponens,[status(thm)],[577, 574])).
% 0.60/0.83 tff(579,plain,
% 0.60/0.83 ((~hskp1) | c0_1(a125)),
% 0.60/0.83 inference(modus_ponens,[status(thm)],[578, 574])).
% 0.60/0.83 tff(580,plain,
% 0.60/0.83 ((~hskp1) | c0_1(a125)),
% 0.60/0.83 inference(modus_ponens,[status(thm)],[579, 574])).
% 0.60/0.83 tff(581,plain,
% 0.60/0.83 (c0_1(a125)),
% 0.60/0.83 inference(unit_resolution,[status(thm)],[580, 559])).
% 0.60/0.83 tff(582,plain,
% 0.60/0.83 (((~![U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp12 | c3_1(a125) | (~ndr1_0) | (~c0_1(a125)) | (~c1_1(a125)))) <=> ((~![U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp12 | c3_1(a125) | (~ndr1_0) | (~c0_1(a125)) | (~c1_1(a125)))),
% 0.60/0.83 inference(rewrite,[status(thm)],[])).
% 0.60/0.83 tff(583,plain,
% 0.60/0.83 ((hskp12 | (~ndr1_0) | c3_1(a125) | (~c1_1(a125)) | (~c0_1(a125))) <=> (hskp12 | c3_1(a125) | (~ndr1_0) | (~c0_1(a125)) | (~c1_1(a125)))),
% 0.60/0.83 inference(rewrite,[status(thm)],[])).
% 0.60/0.83 tff(584,plain,
% 0.60/0.83 (((~![U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp12 | (~ndr1_0) | c3_1(a125) | (~c1_1(a125)) | (~c0_1(a125)))) <=> ((~![U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp12 | c3_1(a125) | (~ndr1_0) | (~c0_1(a125)) | (~c1_1(a125))))),
% 0.60/0.83 inference(monotonicity,[status(thm)],[583])).
% 0.60/0.83 tff(585,plain,
% 0.60/0.83 (((~![U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp12 | (~ndr1_0) | c3_1(a125) | (~c1_1(a125)) | (~c0_1(a125)))) <=> ((~![U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp12 | c3_1(a125) | (~ndr1_0) | (~c0_1(a125)) | (~c1_1(a125)))),
% 0.60/0.83 inference(transitivity,[status(thm)],[584, 582])).
% 0.60/0.83 tff(586,plain,
% 0.60/0.83 ((~![U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp12 | (~ndr1_0) | c3_1(a125) | (~c1_1(a125)) | (~c0_1(a125)))),
% 0.60/0.83 inference(quant_inst,[status(thm)],[])).
% 0.60/0.83 tff(587,plain,
% 0.60/0.83 ((~![U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp12 | c3_1(a125) | (~ndr1_0) | (~c0_1(a125)) | (~c1_1(a125))),
% 0.60/0.83 inference(modus_ponens,[status(thm)],[586, 585])).
% 0.60/0.83 tff(588,plain,
% 0.60/0.83 (hskp12),
% 0.60/0.83 inference(unit_resolution,[status(thm)],[587, 175, 581, 573, 565, 224])).
% 0.60/0.83 tff(589,plain,
% 0.60/0.83 (((~hskp12) | (~c0_1(a140))) <=> ((~hskp12) | (~c0_1(a140)))),
% 0.60/0.83 inference(rewrite,[status(thm)],[])).
% 0.60/0.83 tff(590,plain,
% 0.60/0.83 (((~c0_1(a140)) | (~hskp12)) <=> ((~hskp12) | (~c0_1(a140)))),
% 0.60/0.83 inference(rewrite,[status(thm)],[])).
% 0.60/0.83 tff(591,axiom,((~c0_1(a140)) | (~hskp12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause110')).
% 0.60/0.83 tff(592,plain,
% 0.60/0.83 ((~hskp12) | (~c0_1(a140))),
% 0.60/0.83 inference(modus_ponens,[status(thm)],[591, 590])).
% 0.60/0.83 tff(593,plain,
% 0.60/0.83 ((~hskp12) | (~c0_1(a140))),
% 0.60/0.83 inference(modus_ponens,[status(thm)],[592, 589])).
% 0.60/0.83 tff(594,plain,
% 0.60/0.83 (~c0_1(a140)),
% 0.60/0.83 inference(unit_resolution,[status(thm)],[593, 588])).
% 0.60/0.83 tff(595,assumption,(~c2_1(a149)), introduced(assumption)).
% 0.60/0.83 tff(596,assumption,(~c1_1(a149)), introduced(assumption)).
% 0.60/0.83 tff(597,assumption,(~c2_1(a151)), introduced(assumption)).
% 0.60/0.83 tff(598,plain,
% 0.60/0.83 (((~hskp12) | c3_1(a140)) <=> ((~hskp12) | c3_1(a140))),
% 0.60/0.83 inference(rewrite,[status(thm)],[])).
% 0.60/0.83 tff(599,axiom,((~hskp12) | c3_1(a140)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause66')).
% 0.60/0.83 tff(600,plain,
% 0.60/0.83 ((~hskp12) | c3_1(a140)),
% 0.60/0.83 inference(modus_ponens,[status(thm)],[599, 598])).
% 0.60/0.83 tff(601,plain,
% 0.60/0.83 ((~hskp12) | c3_1(a140)),
% 0.60/0.83 inference(modus_ponens,[status(thm)],[600, 598])).
% 0.60/0.83 tff(602,plain,
% 0.60/0.83 ((~hskp12) | c3_1(a140)),
% 0.60/0.83 inference(modus_ponens,[status(thm)],[601, 598])).
% 0.60/0.83 tff(603,plain,
% 0.60/0.83 ((~hskp12) | c3_1(a140)),
% 0.60/0.83 inference(modus_ponens,[status(thm)],[602, 598])).
% 0.60/0.83 tff(604,plain,
% 0.60/0.83 ((~hskp12) | c3_1(a140)),
% 0.60/0.83 inference(modus_ponens,[status(thm)],[603, 598])).
% 0.60/0.83 tff(605,plain,
% 0.60/0.83 (c3_1(a140)),
% 0.60/0.83 inference(unit_resolution,[status(thm)],[604, 588])).
% 0.60/0.83 tff(606,assumption,(c3_1(a149)), introduced(assumption)).
% 0.60/0.83 tff(607,assumption,(c1_1(a151)), introduced(assumption)).
% 0.60/0.83 tff(608,plain,
% 0.60/0.83 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | (c2_1(a151) | c1_1(a149) | c2_1(a149) | c0_1(a140) | (~ndr1_0) | (~c2_1(a140)) | (~c3_1(a140)) | (~c3_1(a149)) | (~c3_1(a151)) | (~c1_1(a151)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c2_1(a151) | c1_1(a149) | c2_1(a149) | c0_1(a140) | (~ndr1_0) | (~c2_1(a140)) | (~c3_1(a140)) | (~c3_1(a149)) | (~c3_1(a151)) | (~c1_1(a151)))),
% 0.60/0.83 inference(rewrite,[status(thm)],[])).
% 0.60/0.83 tff(609,plain,
% 0.60/0.83 (((~ndr1_0) | c2_1(a151) | (~c3_1(a151)) | (~c1_1(a151)) | c1_1(a149) | c2_1(a149) | (~c3_1(a149)) | c0_1(a140) | (~c2_1(a140)) | (~c3_1(a140))) <=> (c2_1(a151) | c1_1(a149) | c2_1(a149) | c0_1(a140) | (~ndr1_0) | (~c2_1(a140)) | (~c3_1(a140)) | (~c3_1(a149)) | (~c3_1(a151)) | (~c1_1(a151)))),
% 0.60/0.83 inference(rewrite,[status(thm)],[])).
% 0.60/0.83 tff(610,plain,
% 0.60/0.83 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a151) | (~c3_1(a151)) | (~c1_1(a151)) | c1_1(a149) | c2_1(a149) | (~c3_1(a149)) | c0_1(a140) | (~c2_1(a140)) | (~c3_1(a140)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | (c2_1(a151) | c1_1(a149) | c2_1(a149) | c0_1(a140) | (~ndr1_0) | (~c2_1(a140)) | (~c3_1(a140)) | (~c3_1(a149)) | (~c3_1(a151)) | (~c1_1(a151))))),
% 0.60/0.83 inference(monotonicity,[status(thm)],[609])).
% 0.60/0.83 tff(611,plain,
% 0.60/0.83 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a151) | (~c3_1(a151)) | (~c1_1(a151)) | c1_1(a149) | c2_1(a149) | (~c3_1(a149)) | c0_1(a140) | (~c2_1(a140)) | (~c3_1(a140)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c2_1(a151) | c1_1(a149) | c2_1(a149) | c0_1(a140) | (~ndr1_0) | (~c2_1(a140)) | (~c3_1(a140)) | (~c3_1(a149)) | (~c3_1(a151)) | (~c1_1(a151)))),
% 0.60/0.83 inference(transitivity,[status(thm)],[610, 608])).
% 0.60/0.83 tff(612,plain,
% 0.60/0.83 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a151) | (~c3_1(a151)) | (~c1_1(a151)) | c1_1(a149) | c2_1(a149) | (~c3_1(a149)) | c0_1(a140) | (~c2_1(a140)) | (~c3_1(a140)))),
% 0.60/0.83 inference(quant_inst,[status(thm)],[])).
% 0.60/0.83 tff(613,plain,
% 0.60/0.83 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c2_1(a151) | c1_1(a149) | c2_1(a149) | c0_1(a140) | (~ndr1_0) | (~c2_1(a140)) | (~c3_1(a140)) | (~c3_1(a149)) | (~c3_1(a151)) | (~c1_1(a151))),
% 0.60/0.83 inference(modus_ponens,[status(thm)],[612, 611])).
% 0.60/0.83 tff(614,plain,
% 0.60/0.83 (~c2_1(a140)),
% 0.60/0.83 inference(unit_resolution,[status(thm)],[613, 175, 607, 606, 605, 597, 596, 595, 594, 214, 533])).
% 0.60/0.83 tff(615,plain,
% 0.60/0.83 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp3 | c0_1(a140) | (~c2_1(a128)) | c3_1(a128) | (~ndr1_0) | c1_1(a128) | c2_1(a140) | (~c3_1(a140)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp3 | c0_1(a140) | (~c2_1(a128)) | c3_1(a128) | (~ndr1_0) | c1_1(a128) | c2_1(a140) | (~c3_1(a140)))),
% 0.60/0.83 inference(rewrite,[status(thm)],[])).
% 0.60/0.83 tff(616,plain,
% 0.60/0.83 ((hskp3 | (~ndr1_0) | c3_1(a128) | c1_1(a128) | (~c2_1(a128)) | c0_1(a140) | c2_1(a140) | (~c3_1(a140))) <=> (hskp3 | c0_1(a140) | (~c2_1(a128)) | c3_1(a128) | (~ndr1_0) | c1_1(a128) | c2_1(a140) | (~c3_1(a140)))),
% 0.60/0.83 inference(rewrite,[status(thm)],[])).
% 0.60/0.83 tff(617,plain,
% 0.60/0.83 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp3 | (~ndr1_0) | c3_1(a128) | c1_1(a128) | (~c2_1(a128)) | c0_1(a140) | c2_1(a140) | (~c3_1(a140)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp3 | c0_1(a140) | (~c2_1(a128)) | c3_1(a128) | (~ndr1_0) | c1_1(a128) | c2_1(a140) | (~c3_1(a140))))),
% 0.60/0.83 inference(monotonicity,[status(thm)],[616])).
% 0.60/0.83 tff(618,plain,
% 0.60/0.83 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp3 | (~ndr1_0) | c3_1(a128) | c1_1(a128) | (~c2_1(a128)) | c0_1(a140) | c2_1(a140) | (~c3_1(a140)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp3 | c0_1(a140) | (~c2_1(a128)) | c3_1(a128) | (~ndr1_0) | c1_1(a128) | c2_1(a140) | (~c3_1(a140)))),
% 0.60/0.83 inference(transitivity,[status(thm)],[617, 615])).
% 0.60/0.83 tff(619,plain,
% 0.60/0.83 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp3 | (~ndr1_0) | c3_1(a128) | c1_1(a128) | (~c2_1(a128)) | c0_1(a140) | c2_1(a140) | (~c3_1(a140)))),
% 0.60/0.83 inference(quant_inst,[status(thm)],[])).
% 0.60/0.83 tff(620,plain,
% 0.60/0.83 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp3 | c0_1(a140) | (~c2_1(a128)) | c3_1(a128) | (~ndr1_0) | c1_1(a128) | c2_1(a140) | (~c3_1(a140))),
% 0.60/0.83 inference(modus_ponens,[status(thm)],[619, 618])).
% 0.60/0.83 tff(621,plain,
% 0.60/0.83 ($false),
% 0.60/0.83 inference(unit_resolution,[status(thm)],[620, 175, 551, 605, 594, 545, 248, 41, 534, 614])).
% 0.60/0.83 tff(622,plain,(c1_1(a128) | (~c2_1(a128)) | c3_1(a128) | (~c1_1(a151)) | (~c3_1(a149)) | c2_1(a151) | c1_1(a149) | c2_1(a149) | (~c3_1(a151)) | c0_1(a128)), inference(lemma,lemma(discharge,[]))).
% 0.60/0.83 tff(623,plain,
% 0.60/0.83 (c1_1(a128)),
% 0.60/0.83 inference(unit_resolution,[status(thm)],[622, 270, 248, 197, 247, 189, 532, 526, 204, 520])).
% 0.60/0.83 tff(624,assumption,(~hskp1), introduced(assumption)).
% 0.60/0.83 tff(625,assumption,(c1_1(a128)), introduced(assumption)).
% 0.60/0.83 tff(626,plain,
% 0.60/0.83 (^[V: $i, U: $i] : refl((hskp18 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))) <=> (hskp18 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))))),
% 0.60/0.83 inference(bind,[status(th)],[])).
% 0.60/0.83 tff(627,plain,
% 0.60/0.83 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 0.60/0.83 inference(quant_intro,[status(thm)],[626])).
% 0.60/0.83 tff(628,plain,
% 0.60/0.83 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))) <=> ![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 0.60/0.83 inference(rewrite,[status(thm)],[])).
% 0.60/0.83 tff(629,plain,
% 0.60/0.83 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c1_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c0_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)) | (~c1_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c0_1(V)) | hskp18) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))) | hskp18))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V))) | hskp18) <=> (hskp18 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c0_1(V)) | hskp18) <=> (hskp18 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))))),
% 0.60/0.83 inference(bind,[status(th)],[])).
% 0.60/0.83 tff(630,plain,
% 0.60/0.83 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c0_1(V)) | hskp18) <=> ![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 0.60/0.83 inference(quant_intro,[status(thm)],[629])).
% 0.60/0.83 tff(631,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c1_1(V))) | (~c2_1(V))) | c0_1(V)) | hskp18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause175')).
% 0.60/0.83 tff(632,plain,
% 0.60/0.83 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 0.60/0.83 inference(modus_ponens,[status(thm)],[631, 630])).
% 0.60/0.83 tff(633,plain,
% 0.60/0.83 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 0.60/0.83 inference(modus_ponens,[status(thm)],[632, 628])).
% 0.60/0.83 tff(634,plain,(
% 0.60/0.83 ![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 0.60/0.83 inference(skolemize,[status(sab)],[633])).
% 0.60/0.83 tff(635,plain,
% 0.60/0.83 (![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))),
% 0.60/0.83 inference(modus_ponens,[status(thm)],[634, 627])).
% 0.60/0.83 tff(636,assumption,(hskp8), introduced(assumption)).
% 0.60/0.83 tff(637,plain,
% 0.60/0.83 (((~hskp8) | c3_1(a135)) <=> ((~hskp8) | c3_1(a135))),
% 0.60/0.83 inference(rewrite,[status(thm)],[])).
% 0.60/0.83 tff(638,axiom,((~hskp8) | c3_1(a135)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause73')).
% 0.60/0.83 tff(639,plain,
% 0.60/0.83 ((~hskp8) | c3_1(a135)),
% 0.60/0.83 inference(modus_ponens,[status(thm)],[638, 637])).
% 0.60/0.83 tff(640,plain,
% 0.60/0.83 ((~hskp8) | c3_1(a135)),
% 0.60/0.83 inference(modus_ponens,[status(thm)],[639, 637])).
% 0.60/0.83 tff(641,plain,
% 0.60/0.83 ((~hskp8) | c3_1(a135)),
% 0.60/0.83 inference(modus_ponens,[status(thm)],[640, 637])).
% 0.60/0.83 tff(642,plain,
% 0.60/0.83 ((~hskp8) | c3_1(a135)),
% 0.60/0.83 inference(modus_ponens,[status(thm)],[641, 637])).
% 0.60/0.83 tff(643,plain,
% 0.60/0.83 ((~hskp8) | c3_1(a135)),
% 0.60/0.83 inference(modus_ponens,[status(thm)],[642, 637])).
% 0.60/0.83 tff(644,plain,
% 0.60/0.83 (c3_1(a135)),
% 0.60/0.83 inference(unit_resolution,[status(thm)],[643, 636])).
% 0.60/0.83 tff(645,plain,
% 0.60/0.83 (((~hskp8) | c2_1(a135)) <=> ((~hskp8) | c2_1(a135))),
% 0.60/0.83 inference(rewrite,[status(thm)],[])).
% 0.60/0.83 tff(646,axiom,((~hskp8) | c2_1(a135)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause72')).
% 0.60/0.83 tff(647,plain,
% 0.60/0.83 ((~hskp8) | c2_1(a135)),
% 0.60/0.83 inference(modus_ponens,[status(thm)],[646, 645])).
% 0.60/0.83 tff(648,plain,
% 0.60/0.83 ((~hskp8) | c2_1(a135)),
% 0.60/0.83 inference(modus_ponens,[status(thm)],[647, 645])).
% 0.60/0.83 tff(649,plain,
% 0.60/0.83 ((~hskp8) | c2_1(a135)),
% 0.60/0.83 inference(modus_ponens,[status(thm)],[648, 645])).
% 0.60/0.83 tff(650,plain,
% 0.60/0.83 ((~hskp8) | c2_1(a135)),
% 0.60/0.83 inference(modus_ponens,[status(thm)],[649, 645])).
% 0.60/0.83 tff(651,plain,
% 0.60/0.83 ((~hskp8) | c2_1(a135)),
% 0.60/0.83 inference(modus_ponens,[status(thm)],[650, 645])).
% 0.60/0.83 tff(652,plain,
% 0.60/0.83 (c2_1(a135)),
% 0.60/0.83 inference(unit_resolution,[status(thm)],[651, 636])).
% 0.60/0.83 tff(653,plain,
% 0.60/0.83 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp18 | c0_1(a128) | (~c2_1(a128)) | (~ndr1_0) | (~c1_1(a128)) | (~c3_1(a135)) | (~c2_1(a135)) | (~c0_1(a135)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp18 | c0_1(a128) | (~c2_1(a128)) | (~ndr1_0) | (~c1_1(a128)) | (~c3_1(a135)) | (~c2_1(a135)) | (~c0_1(a135)))),
% 0.60/0.83 inference(rewrite,[status(thm)],[])).
% 0.60/0.83 tff(654,plain,
% 0.60/0.83 ((hskp18 | (~ndr1_0) | (~c2_1(a135)) | (~c3_1(a135)) | (~c0_1(a135)) | c0_1(a128) | (~c2_1(a128)) | (~c1_1(a128))) <=> (hskp18 | c0_1(a128) | (~c2_1(a128)) | (~ndr1_0) | (~c1_1(a128)) | (~c3_1(a135)) | (~c2_1(a135)) | (~c0_1(a135)))),
% 0.60/0.83 inference(rewrite,[status(thm)],[])).
% 0.60/0.83 tff(655,plain,
% 0.60/0.83 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp18 | (~ndr1_0) | (~c2_1(a135)) | (~c3_1(a135)) | (~c0_1(a135)) | c0_1(a128) | (~c2_1(a128)) | (~c1_1(a128)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp18 | c0_1(a128) | (~c2_1(a128)) | (~ndr1_0) | (~c1_1(a128)) | (~c3_1(a135)) | (~c2_1(a135)) | (~c0_1(a135))))),
% 0.60/0.83 inference(monotonicity,[status(thm)],[654])).
% 0.60/0.83 tff(656,plain,
% 0.60/0.83 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp18 | (~ndr1_0) | (~c2_1(a135)) | (~c3_1(a135)) | (~c0_1(a135)) | c0_1(a128) | (~c2_1(a128)) | (~c1_1(a128)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp18 | c0_1(a128) | (~c2_1(a128)) | (~ndr1_0) | (~c1_1(a128)) | (~c3_1(a135)) | (~c2_1(a135)) | (~c0_1(a135)))),
% 0.60/0.83 inference(transitivity,[status(thm)],[655, 653])).
% 0.60/0.83 tff(657,plain,
% 0.60/0.83 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp18 | (~ndr1_0) | (~c2_1(a135)) | (~c3_1(a135)) | (~c0_1(a135)) | c0_1(a128) | (~c2_1(a128)) | (~c1_1(a128)))),
% 0.60/0.83 inference(quant_inst,[status(thm)],[])).
% 0.60/0.83 tff(658,plain,
% 0.60/0.83 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp18 | c0_1(a128) | (~c2_1(a128)) | (~ndr1_0) | (~c1_1(a128)) | (~c3_1(a135)) | (~c2_1(a135)) | (~c0_1(a135))),
% 0.60/0.83 inference(modus_ponens,[status(thm)],[657, 656])).
% 0.60/0.83 tff(659,plain,
% 0.60/0.83 (~c0_1(a135)),
% 0.60/0.83 inference(unit_resolution,[status(thm)],[658, 175, 95, 652, 644, 270, 545, 635, 625])).
% 0.60/0.83 tff(660,plain,
% 0.60/0.83 (((~hskp8) | (~c1_1(a135))) <=> ((~hskp8) | (~c1_1(a135)))),
% 0.60/0.83 inference(rewrite,[status(thm)],[])).
% 0.60/0.83 tff(661,plain,
% 0.60/0.83 (((~c1_1(a135)) | (~hskp8)) <=> ((~hskp8) | (~c1_1(a135)))),
% 0.60/0.83 inference(rewrite,[status(thm)],[])).
% 0.60/0.83 tff(662,axiom,((~c1_1(a135)) | (~hskp8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause115')).
% 0.60/0.83 tff(663,plain,
% 0.60/0.83 ((~hskp8) | (~c1_1(a135))),
% 0.60/0.83 inference(modus_ponens,[status(thm)],[662, 661])).
% 0.60/0.83 tff(664,plain,
% 0.60/0.83 ((~hskp8) | (~c1_1(a135))),
% 0.60/0.83 inference(modus_ponens,[status(thm)],[663, 660])).
% 0.60/0.83 tff(665,plain,
% 0.60/0.83 (~c1_1(a135)),
% 0.60/0.83 inference(unit_resolution,[status(thm)],[664, 636])).
% 0.60/0.83 tff(666,plain,
% 0.60/0.83 (((~![U: $i] : (hskp3 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp3 | hskp1 | c1_1(a135) | (~ndr1_0) | (~c2_1(a135)) | c0_1(a135))) <=> ((~![U: $i] : (hskp3 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp3 | hskp1 | c1_1(a135) | (~ndr1_0) | (~c2_1(a135)) | c0_1(a135))),
% 0.60/0.83 inference(rewrite,[status(thm)],[])).
% 0.60/0.83 tff(667,plain,
% 0.60/0.83 ((hskp3 | hskp1 | (~ndr1_0) | c1_1(a135) | c0_1(a135) | (~c2_1(a135))) <=> (hskp3 | hskp1 | c1_1(a135) | (~ndr1_0) | (~c2_1(a135)) | c0_1(a135))),
% 0.60/0.83 inference(rewrite,[status(thm)],[])).
% 0.60/0.83 tff(668,plain,
% 0.60/0.83 (((~![U: $i] : (hskp3 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp3 | hskp1 | (~ndr1_0) | c1_1(a135) | c0_1(a135) | (~c2_1(a135)))) <=> ((~![U: $i] : (hskp3 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp3 | hskp1 | c1_1(a135) | (~ndr1_0) | (~c2_1(a135)) | c0_1(a135)))),
% 0.60/0.84 inference(monotonicity,[status(thm)],[667])).
% 0.60/0.84 tff(669,plain,
% 0.60/0.84 (((~![U: $i] : (hskp3 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp3 | hskp1 | (~ndr1_0) | c1_1(a135) | c0_1(a135) | (~c2_1(a135)))) <=> ((~![U: $i] : (hskp3 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp3 | hskp1 | c1_1(a135) | (~ndr1_0) | (~c2_1(a135)) | c0_1(a135))),
% 0.60/0.84 inference(transitivity,[status(thm)],[668, 666])).
% 0.60/0.84 tff(670,plain,
% 0.60/0.84 ((~![U: $i] : (hskp3 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp3 | hskp1 | (~ndr1_0) | c1_1(a135) | c0_1(a135) | (~c2_1(a135)))),
% 0.60/0.84 inference(quant_inst,[status(thm)],[])).
% 0.60/0.84 tff(671,plain,
% 0.60/0.84 ((~![U: $i] : (hskp3 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp3 | hskp1 | c1_1(a135) | (~ndr1_0) | (~c2_1(a135)) | c0_1(a135)),
% 0.60/0.84 inference(modus_ponens,[status(thm)],[670, 669])).
% 0.60/0.84 tff(672,plain,
% 0.60/0.84 ($false),
% 0.60/0.84 inference(unit_resolution,[status(thm)],[671, 175, 551, 624, 652, 665, 544, 659])).
% 0.60/0.84 tff(673,plain,((~hskp8) | hskp1 | hskp18 | c0_1(a128) | (~c2_1(a128)) | (~c1_1(a128))), inference(lemma,lemma(discharge,[]))).
% 0.60/0.84 tff(674,plain,
% 0.60/0.84 (~hskp8),
% 0.60/0.84 inference(unit_resolution,[status(thm)],[673, 624, 95, 270, 520, 623])).
% 0.60/0.84 tff(675,plain,
% 0.60/0.84 (^[V: $i, U: $i] : refl((hskp8 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))) <=> (hskp8 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))))),
% 0.60/0.84 inference(bind,[status(th)],[])).
% 0.60/0.84 tff(676,plain,
% 0.60/0.84 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 0.60/0.84 inference(quant_intro,[status(thm)],[675])).
% 0.60/0.84 tff(677,plain,
% 0.60/0.84 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 0.60/0.84 inference(rewrite,[status(thm)],[])).
% 0.60/0.84 tff(678,plain,
% 0.60/0.84 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | (~c2_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V))))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))), ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | hskp8) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))) | hskp8))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V))) | hskp8) <=> (hskp8 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))), (((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | hskp8) <=> (hskp8 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))))),
% 0.60/0.84 inference(bind,[status(th)],[])).
% 0.60/0.84 tff(679,plain,
% 0.60/0.84 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | hskp8) <=> ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 0.60/0.84 inference(quant_intro,[status(thm)],[678])).
% 0.60/0.84 tff(680,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | c3_1(V)) | hskp8)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause169')).
% 0.60/0.84 tff(681,plain,
% 0.60/0.84 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 0.60/0.84 inference(modus_ponens,[status(thm)],[680, 679])).
% 0.60/0.84 tff(682,plain,
% 0.60/0.84 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 0.60/0.84 inference(modus_ponens,[status(thm)],[681, 677])).
% 0.60/0.84 tff(683,plain,(
% 0.60/0.84 ![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 0.60/0.84 inference(skolemize,[status(sab)],[682])).
% 0.60/0.84 tff(684,plain,
% 0.60/0.84 (![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))),
% 0.60/0.84 inference(modus_ponens,[status(thm)],[683, 676])).
% 0.60/0.84 tff(685,plain,
% 0.60/0.84 (~hskp3),
% 0.60/0.84 inference(unit_resolution,[status(thm)],[550, 520])).
% 0.60/0.84 tff(686,assumption,(hskp14), introduced(assumption)).
% 0.60/0.84 tff(687,plain,
% 0.60/0.84 (~c1_1(a145)),
% 0.60/0.84 inference(unit_resolution,[status(thm)],[495, 686])).
% 0.60/0.84 tff(688,plain,
% 0.60/0.84 (~c0_1(a145)),
% 0.60/0.84 inference(unit_resolution,[status(thm)],[508, 686])).
% 0.60/0.84 tff(689,plain,
% 0.60/0.84 (((~![U: $i] : (hskp3 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp3 | hskp1 | c0_1(a145) | c1_1(a145) | (~ndr1_0) | (~c2_1(a145)))) <=> ((~![U: $i] : (hskp3 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp3 | hskp1 | c0_1(a145) | c1_1(a145) | (~ndr1_0) | (~c2_1(a145)))),
% 0.60/0.84 inference(rewrite,[status(thm)],[])).
% 0.60/0.84 tff(690,plain,
% 0.60/0.84 ((hskp3 | hskp1 | (~ndr1_0) | c1_1(a145) | c0_1(a145) | (~c2_1(a145))) <=> (hskp3 | hskp1 | c0_1(a145) | c1_1(a145) | (~ndr1_0) | (~c2_1(a145)))),
% 0.60/0.84 inference(rewrite,[status(thm)],[])).
% 0.60/0.84 tff(691,plain,
% 0.60/0.84 (((~![U: $i] : (hskp3 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp3 | hskp1 | (~ndr1_0) | c1_1(a145) | c0_1(a145) | (~c2_1(a145)))) <=> ((~![U: $i] : (hskp3 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp3 | hskp1 | c0_1(a145) | c1_1(a145) | (~ndr1_0) | (~c2_1(a145))))),
% 0.60/0.84 inference(monotonicity,[status(thm)],[690])).
% 0.60/0.84 tff(692,plain,
% 0.60/0.84 (((~![U: $i] : (hskp3 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp3 | hskp1 | (~ndr1_0) | c1_1(a145) | c0_1(a145) | (~c2_1(a145)))) <=> ((~![U: $i] : (hskp3 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp3 | hskp1 | c0_1(a145) | c1_1(a145) | (~ndr1_0) | (~c2_1(a145)))),
% 0.60/0.84 inference(transitivity,[status(thm)],[691, 689])).
% 0.60/0.84 tff(693,plain,
% 0.60/0.84 ((~![U: $i] : (hskp3 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp3 | hskp1 | (~ndr1_0) | c1_1(a145) | c0_1(a145) | (~c2_1(a145)))),
% 0.60/0.84 inference(quant_inst,[status(thm)],[])).
% 0.60/0.84 tff(694,plain,
% 0.60/0.84 ((~![U: $i] : (hskp3 | hskp1 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c2_1(U)))) | hskp3 | hskp1 | c0_1(a145) | c1_1(a145) | (~ndr1_0) | (~c2_1(a145))),
% 0.60/0.84 inference(modus_ponens,[status(thm)],[693, 692])).
% 0.60/0.84 tff(695,plain,
% 0.60/0.84 (~c2_1(a145)),
% 0.60/0.84 inference(unit_resolution,[status(thm)],[694, 175, 52, 624, 688, 687, 544])).
% 0.60/0.84 tff(696,plain,
% 0.60/0.84 (~c3_1(a145)),
% 0.60/0.84 inference(unit_resolution,[status(thm)],[489, 686])).
% 0.60/0.84 tff(697,plain,
% 0.60/0.84 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a149) | c2_1(a149) | c0_1(a145) | c3_1(a145) | c1_1(a138) | (~ndr1_0) | (~c3_1(a138)) | (~c0_1(a138)) | c2_1(a145) | c0_1(a149))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a149) | c2_1(a149) | c0_1(a145) | c3_1(a145) | c1_1(a138) | (~ndr1_0) | (~c3_1(a138)) | (~c0_1(a138)) | c2_1(a145) | c0_1(a149))),
% 0.60/0.84 inference(rewrite,[status(thm)],[])).
% 0.60/0.84 tff(698,plain,
% 0.60/0.84 (((~ndr1_0) | c1_1(a138) | (~c3_1(a138)) | (~c0_1(a138)) | c3_1(a145) | c0_1(a145) | c2_1(a145) | c2_1(a149) | c1_1(a149) | c0_1(a149)) <=> (c1_1(a149) | c2_1(a149) | c0_1(a145) | c3_1(a145) | c1_1(a138) | (~ndr1_0) | (~c3_1(a138)) | (~c0_1(a138)) | c2_1(a145) | c0_1(a149))),
% 0.60/0.84 inference(rewrite,[status(thm)],[])).
% 0.60/0.84 tff(699,plain,
% 0.60/0.84 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a138) | (~c3_1(a138)) | (~c0_1(a138)) | c3_1(a145) | c0_1(a145) | c2_1(a145) | c2_1(a149) | c1_1(a149) | c0_1(a149))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a149) | c2_1(a149) | c0_1(a145) | c3_1(a145) | c1_1(a138) | (~ndr1_0) | (~c3_1(a138)) | (~c0_1(a138)) | c2_1(a145) | c0_1(a149)))),
% 0.60/0.84 inference(monotonicity,[status(thm)],[698])).
% 0.60/0.84 tff(700,plain,
% 0.60/0.84 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a138) | (~c3_1(a138)) | (~c0_1(a138)) | c3_1(a145) | c0_1(a145) | c2_1(a145) | c2_1(a149) | c1_1(a149) | c0_1(a149))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a149) | c2_1(a149) | c0_1(a145) | c3_1(a145) | c1_1(a138) | (~ndr1_0) | (~c3_1(a138)) | (~c0_1(a138)) | c2_1(a145) | c0_1(a149))),
% 0.60/0.84 inference(transitivity,[status(thm)],[699, 697])).
% 0.60/0.84 tff(701,plain,
% 0.60/0.84 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a138) | (~c3_1(a138)) | (~c0_1(a138)) | c3_1(a145) | c0_1(a145) | c2_1(a145) | c2_1(a149) | c1_1(a149) | c0_1(a149))),
% 0.60/0.84 inference(quant_inst,[status(thm)],[])).
% 0.60/0.84 tff(702,plain,
% 0.60/0.84 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a149) | c2_1(a149) | c0_1(a145) | c3_1(a145) | c1_1(a138) | (~ndr1_0) | (~c3_1(a138)) | (~c0_1(a138)) | c2_1(a145) | c0_1(a149)),
% 0.60/0.84 inference(modus_ponens,[status(thm)],[701, 700])).
% 0.60/0.84 tff(703,plain,
% 0.60/0.84 (c0_1(a149)),
% 0.60/0.84 inference(unit_resolution,[status(thm)],[702, 175, 141, 140, 596, 595, 688, 696, 139, 258, 695])).
% 0.60/0.84 tff(704,plain,
% 0.60/0.84 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a149) | c0_1(a145) | c1_1(a145) | c3_1(a145) | (~ndr1_0) | c2_1(a145) | (~c3_1(a149)) | (~c0_1(a149)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a149) | c0_1(a145) | c1_1(a145) | c3_1(a145) | (~ndr1_0) | c2_1(a145) | (~c3_1(a149)) | (~c0_1(a149)))),
% 0.60/0.84 inference(rewrite,[status(thm)],[])).
% 0.60/0.84 tff(705,plain,
% 0.60/0.84 (((~ndr1_0) | c1_1(a149) | (~c3_1(a149)) | (~c0_1(a149)) | c3_1(a145) | c0_1(a145) | c2_1(a145) | c2_1(a145) | c1_1(a145) | c0_1(a145)) <=> (c1_1(a149) | c0_1(a145) | c1_1(a145) | c3_1(a145) | (~ndr1_0) | c2_1(a145) | (~c3_1(a149)) | (~c0_1(a149)))),
% 0.60/0.84 inference(rewrite,[status(thm)],[])).
% 0.60/0.84 tff(706,plain,
% 0.60/0.84 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a149) | (~c3_1(a149)) | (~c0_1(a149)) | c3_1(a145) | c0_1(a145) | c2_1(a145) | c2_1(a145) | c1_1(a145) | c0_1(a145))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a149) | c0_1(a145) | c1_1(a145) | c3_1(a145) | (~ndr1_0) | c2_1(a145) | (~c3_1(a149)) | (~c0_1(a149))))),
% 0.60/0.84 inference(monotonicity,[status(thm)],[705])).
% 0.60/0.84 tff(707,plain,
% 0.60/0.84 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a149) | (~c3_1(a149)) | (~c0_1(a149)) | c3_1(a145) | c0_1(a145) | c2_1(a145) | c2_1(a145) | c1_1(a145) | c0_1(a145))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a149) | c0_1(a145) | c1_1(a145) | c3_1(a145) | (~ndr1_0) | c2_1(a145) | (~c3_1(a149)) | (~c0_1(a149)))),
% 0.60/0.84 inference(transitivity,[status(thm)],[706, 704])).
% 0.60/0.84 tff(708,plain,
% 0.60/0.84 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a149) | (~c3_1(a149)) | (~c0_1(a149)) | c3_1(a145) | c0_1(a145) | c2_1(a145) | c2_1(a145) | c1_1(a145) | c0_1(a145))),
% 0.60/0.84 inference(quant_inst,[status(thm)],[])).
% 0.60/0.84 tff(709,plain,
% 0.60/0.84 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a149) | c0_1(a145) | c1_1(a145) | c3_1(a145) | (~ndr1_0) | c2_1(a145) | (~c3_1(a149)) | (~c0_1(a149))),
% 0.60/0.84 inference(modus_ponens,[status(thm)],[708, 707])).
% 0.60/0.84 tff(710,plain,
% 0.60/0.84 ($false),
% 0.60/0.84 inference(unit_resolution,[status(thm)],[709, 175, 606, 596, 688, 687, 696, 258, 703, 695])).
% 0.60/0.84 tff(711,plain,((~hskp14) | (~c3_1(a149)) | c1_1(a149) | (~c0_1(a138)) | (~c3_1(a138)) | c2_1(a149) | c1_1(a138) | hskp3 | hskp1), inference(lemma,lemma(discharge,[]))).
% 0.60/0.84 tff(712,plain,
% 0.60/0.84 (~hskp14),
% 0.60/0.84 inference(unit_resolution,[status(thm)],[711, 624, 532, 141, 140, 526, 139, 685, 247])).
% 0.60/0.84 tff(713,plain,
% 0.60/0.84 (((~![U: $i] : (hskp14 | hskp3 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp14 | hskp3 | c2_1(a149) | (~ndr1_0) | (~c3_1(a149)) | c0_1(a149))) <=> ((~![U: $i] : (hskp14 | hskp3 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | hskp14 | hskp3 | c2_1(a149) | (~ndr1_0) | (~c3_1(a149)) | c0_1(a149))),
% 0.60/0.84 inference(rewrite,[status(thm)],[])).
% 0.60/0.84 tff(714,plain,
% 0.60/0.84 ((hskp14 | hskp3 | (~ndr1_0) | c0_1(a149) | c2_1(a149) | (~c3_1(a149))) <=> (hskp14 | hskp3 | c2_1(a149) | (~ndr1_0) | (~c3_1(a149)) | c0_1(a149))),
% 0.60/0.84 inference(rewrite,[status(thm)],[])).
% 0.60/0.84 tff(715,plain,
% 0.60/0.84 (((~![U: $i] : (hskp14 | hskp3 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp14 | hskp3 | (~ndr1_0) | c0_1(a149) | c2_1(a149) | (~c3_1(a149)))) <=> ((~![U: $i] : (hskp14 | hskp3 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp14 | hskp3 | c2_1(a149) | (~ndr1_0) | (~c3_1(a149)) | c0_1(a149)))),
% 0.60/0.84 inference(monotonicity,[status(thm)],[714])).
% 0.60/0.84 tff(716,plain,
% 0.60/0.84 (((~![U: $i] : (hskp14 | hskp3 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp14 | hskp3 | (~ndr1_0) | c0_1(a149) | c2_1(a149) | (~c3_1(a149)))) <=> ((~![U: $i] : (hskp14 | hskp3 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | hskp14 | hskp3 | c2_1(a149) | (~ndr1_0) | (~c3_1(a149)) | c0_1(a149))),
% 0.60/0.84 inference(transitivity,[status(thm)],[715, 713])).
% 0.60/0.84 tff(717,plain,
% 0.60/0.84 ((~![U: $i] : (hskp14 | hskp3 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp14 | hskp3 | (~ndr1_0) | c0_1(a149) | c2_1(a149) | (~c3_1(a149)))),
% 0.60/0.84 inference(quant_inst,[status(thm)],[])).
% 0.60/0.84 tff(718,plain,
% 0.60/0.84 ((~![U: $i] : (hskp14 | hskp3 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | hskp14 | hskp3 | c2_1(a149) | (~ndr1_0) | (~c3_1(a149)) | c0_1(a149)),
% 0.60/0.84 inference(modus_ponens,[status(thm)],[717, 716])).
% 0.60/0.84 tff(719,plain,
% 0.60/0.84 (hskp14 | c0_1(a149)),
% 0.60/0.84 inference(unit_resolution,[status(thm)],[718, 175, 685, 247, 526, 51])).
% 0.60/0.84 tff(720,plain,
% 0.60/0.84 (c0_1(a149)),
% 0.60/0.84 inference(unit_resolution,[status(thm)],[719, 712])).
% 0.60/0.84 tff(721,assumption,(hskp6), introduced(assumption)).
% 0.60/0.84 tff(722,plain,
% 0.60/0.84 (~c2_1(a133)),
% 0.60/0.84 inference(unit_resolution,[status(thm)],[336, 721])).
% 0.60/0.84 tff(723,plain,
% 0.60/0.84 (~c0_1(a133)),
% 0.60/0.84 inference(unit_resolution,[status(thm)],[348, 721])).
% 0.60/0.84 tff(724,assumption,(~hskp14), introduced(assumption)).
% 0.60/0.84 tff(725,plain,
% 0.60/0.84 (((~![U: $i] : (hskp14 | hskp3 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp14 | hskp3 | c0_1(a133) | c2_1(a133) | (~ndr1_0) | (~c3_1(a133)))) <=> ((~![U: $i] : (hskp14 | hskp3 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | hskp14 | hskp3 | c0_1(a133) | c2_1(a133) | (~ndr1_0) | (~c3_1(a133)))),
% 0.60/0.84 inference(rewrite,[status(thm)],[])).
% 0.60/0.84 tff(726,plain,
% 0.60/0.84 ((hskp14 | hskp3 | (~ndr1_0) | c0_1(a133) | c2_1(a133) | (~c3_1(a133))) <=> (hskp14 | hskp3 | c0_1(a133) | c2_1(a133) | (~ndr1_0) | (~c3_1(a133)))),
% 0.60/0.84 inference(rewrite,[status(thm)],[])).
% 0.60/0.84 tff(727,plain,
% 0.60/0.84 (((~![U: $i] : (hskp14 | hskp3 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp14 | hskp3 | (~ndr1_0) | c0_1(a133) | c2_1(a133) | (~c3_1(a133)))) <=> ((~![U: $i] : (hskp14 | hskp3 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp14 | hskp3 | c0_1(a133) | c2_1(a133) | (~ndr1_0) | (~c3_1(a133))))),
% 0.60/0.84 inference(monotonicity,[status(thm)],[726])).
% 0.60/0.84 tff(728,plain,
% 0.60/0.84 (((~![U: $i] : (hskp14 | hskp3 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp14 | hskp3 | (~ndr1_0) | c0_1(a133) | c2_1(a133) | (~c3_1(a133)))) <=> ((~![U: $i] : (hskp14 | hskp3 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | hskp14 | hskp3 | c0_1(a133) | c2_1(a133) | (~ndr1_0) | (~c3_1(a133)))),
% 0.60/0.84 inference(transitivity,[status(thm)],[727, 725])).
% 0.60/0.84 tff(729,plain,
% 0.60/0.84 ((~![U: $i] : (hskp14 | hskp3 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp14 | hskp3 | (~ndr1_0) | c0_1(a133) | c2_1(a133) | (~c3_1(a133)))),
% 0.60/0.84 inference(quant_inst,[status(thm)],[])).
% 0.60/0.84 tff(730,plain,
% 0.60/0.84 ((~![U: $i] : (hskp14 | hskp3 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | hskp14 | hskp3 | c0_1(a133) | c2_1(a133) | (~ndr1_0) | (~c3_1(a133))),
% 0.60/0.84 inference(modus_ponens,[status(thm)],[729, 728])).
% 0.60/0.84 tff(731,plain,
% 0.60/0.84 (~c3_1(a133)),
% 0.60/0.84 inference(unit_resolution,[status(thm)],[730, 175, 724, 52, 723, 722, 51])).
% 0.60/0.84 tff(732,assumption,(c0_1(a149)), introduced(assumption)).
% 0.60/0.84 tff(733,plain,
% 0.60/0.84 (~c1_1(a133)),
% 0.60/0.84 inference(unit_resolution,[status(thm)],[342, 721])).
% 0.60/0.84 tff(734,plain,
% 0.60/0.84 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a149) | c0_1(a133) | c1_1(a133) | c2_1(a133) | (~ndr1_0) | c3_1(a133) | (~c3_1(a149)) | (~c0_1(a149)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a149) | c0_1(a133) | c1_1(a133) | c2_1(a133) | (~ndr1_0) | c3_1(a133) | (~c3_1(a149)) | (~c0_1(a149)))),
% 0.60/0.84 inference(rewrite,[status(thm)],[])).
% 0.60/0.84 tff(735,plain,
% 0.60/0.84 (((~ndr1_0) | c1_1(a149) | (~c3_1(a149)) | (~c0_1(a149)) | c3_1(a133) | c0_1(a133) | c2_1(a133) | c2_1(a133) | c1_1(a133) | c0_1(a133)) <=> (c1_1(a149) | c0_1(a133) | c1_1(a133) | c2_1(a133) | (~ndr1_0) | c3_1(a133) | (~c3_1(a149)) | (~c0_1(a149)))),
% 0.60/0.84 inference(rewrite,[status(thm)],[])).
% 0.60/0.84 tff(736,plain,
% 0.60/0.84 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a149) | (~c3_1(a149)) | (~c0_1(a149)) | c3_1(a133) | c0_1(a133) | c2_1(a133) | c2_1(a133) | c1_1(a133) | c0_1(a133))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a149) | c0_1(a133) | c1_1(a133) | c2_1(a133) | (~ndr1_0) | c3_1(a133) | (~c3_1(a149)) | (~c0_1(a149))))),
% 0.60/0.84 inference(monotonicity,[status(thm)],[735])).
% 0.60/0.84 tff(737,plain,
% 0.60/0.84 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a149) | (~c3_1(a149)) | (~c0_1(a149)) | c3_1(a133) | c0_1(a133) | c2_1(a133) | c2_1(a133) | c1_1(a133) | c0_1(a133))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a149) | c0_1(a133) | c1_1(a133) | c2_1(a133) | (~ndr1_0) | c3_1(a133) | (~c3_1(a149)) | (~c0_1(a149)))),
% 0.60/0.84 inference(transitivity,[status(thm)],[736, 734])).
% 0.60/0.84 tff(738,plain,
% 0.60/0.84 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a149) | (~c3_1(a149)) | (~c0_1(a149)) | c3_1(a133) | c0_1(a133) | c2_1(a133) | c2_1(a133) | c1_1(a133) | c0_1(a133))),
% 0.60/0.84 inference(quant_inst,[status(thm)],[])).
% 0.60/0.84 tff(739,plain,
% 0.60/0.84 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a149) | c0_1(a133) | c1_1(a133) | c2_1(a133) | (~ndr1_0) | c3_1(a133) | (~c3_1(a149)) | (~c0_1(a149))),
% 0.60/0.84 inference(modus_ponens,[status(thm)],[738, 737])).
% 0.60/0.84 tff(740,plain,
% 0.60/0.84 ($false),
% 0.60/0.84 inference(unit_resolution,[status(thm)],[739, 175, 606, 596, 723, 733, 722, 258, 732, 731])).
% 0.60/0.84 tff(741,plain,((~hskp6) | (~c3_1(a149)) | c1_1(a149) | (~c0_1(a149)) | hskp14 | hskp3), inference(lemma,lemma(discharge,[]))).
% 0.60/0.84 tff(742,plain,
% 0.60/0.84 (~hskp6),
% 0.60/0.84 inference(unit_resolution,[status(thm)],[741, 720, 532, 247, 712, 685])).
% 0.60/0.84 tff(743,plain,
% 0.60/0.84 ((hskp21 | hskp9 | hskp6) <=> (hskp21 | hskp9 | hskp6)),
% 0.60/0.84 inference(rewrite,[status(thm)],[])).
% 0.60/0.84 tff(744,plain,
% 0.60/0.84 (((hskp21 | hskp9) | hskp6) <=> (hskp21 | hskp9 | hskp6)),
% 0.60/0.84 inference(rewrite,[status(thm)],[])).
% 0.60/0.84 tff(745,plain,
% 0.60/0.84 ((hskp9 | hskp21) <=> (hskp21 | hskp9)),
% 0.60/0.84 inference(rewrite,[status(thm)],[])).
% 0.60/0.84 tff(746,plain,
% 0.60/0.84 (((hskp9 | hskp21) | hskp6) <=> ((hskp21 | hskp9) | hskp6)),
% 0.60/0.84 inference(monotonicity,[status(thm)],[745])).
% 0.60/0.84 tff(747,plain,
% 0.60/0.84 (((hskp9 | hskp21) | hskp6) <=> (hskp21 | hskp9 | hskp6)),
% 0.60/0.84 inference(transitivity,[status(thm)],[746, 744])).
% 0.60/0.84 tff(748,axiom,((hskp9 | hskp21) | hskp6), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause34')).
% 0.60/0.84 tff(749,plain,
% 0.60/0.84 (hskp21 | hskp9 | hskp6),
% 0.60/0.84 inference(modus_ponens,[status(thm)],[748, 747])).
% 0.60/0.84 tff(750,plain,
% 0.60/0.84 (hskp21 | hskp9 | hskp6),
% 0.60/0.84 inference(modus_ponens,[status(thm)],[749, 743])).
% 0.60/0.84 tff(751,plain,
% 0.60/0.84 (hskp21 | hskp9 | hskp6),
% 0.60/0.84 inference(modus_ponens,[status(thm)],[750, 743])).
% 0.60/0.84 tff(752,plain,
% 0.60/0.84 (hskp21 | hskp9 | hskp6),
% 0.60/0.84 inference(modus_ponens,[status(thm)],[751, 743])).
% 0.60/0.84 tff(753,plain,
% 0.60/0.84 (hskp21 | hskp9 | hskp6),
% 0.60/0.84 inference(modus_ponens,[status(thm)],[752, 743])).
% 0.60/0.84 tff(754,plain,
% 0.60/0.84 (hskp9),
% 0.60/0.84 inference(unit_resolution,[status(thm)],[753, 742, 53])).
% 0.60/0.84 tff(755,plain,
% 0.60/0.84 (((~hskp9) | (~c3_1(a136))) <=> ((~hskp9) | (~c3_1(a136)))),
% 0.60/0.84 inference(rewrite,[status(thm)],[])).
% 0.60/0.84 tff(756,plain,
% 0.60/0.84 (((~c3_1(a136)) | (~hskp9)) <=> ((~hskp9) | (~c3_1(a136)))),
% 0.60/0.84 inference(rewrite,[status(thm)],[])).
% 0.60/0.84 tff(757,axiom,((~c3_1(a136)) | (~hskp9)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause114')).
% 0.60/0.84 tff(758,plain,
% 0.60/0.84 ((~hskp9) | (~c3_1(a136))),
% 0.60/0.84 inference(modus_ponens,[status(thm)],[757, 756])).
% 0.60/0.84 tff(759,plain,
% 0.60/0.84 ((~hskp9) | (~c3_1(a136))),
% 0.60/0.84 inference(modus_ponens,[status(thm)],[758, 755])).
% 0.60/0.84 tff(760,plain,
% 0.60/0.84 (~c3_1(a136)),
% 0.60/0.84 inference(unit_resolution,[status(thm)],[759, 754])).
% 0.60/0.84 tff(761,plain,
% 0.60/0.84 (((~hskp9) | c2_1(a136)) <=> ((~hskp9) | c2_1(a136))),
% 0.60/0.84 inference(rewrite,[status(thm)],[])).
% 0.60/0.84 tff(762,axiom,((~hskp9) | c2_1(a136)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause71')).
% 0.60/0.84 tff(763,plain,
% 0.60/0.84 ((~hskp9) | c2_1(a136)),
% 0.60/0.84 inference(modus_ponens,[status(thm)],[762, 761])).
% 0.60/0.84 tff(764,plain,
% 0.60/0.84 ((~hskp9) | c2_1(a136)),
% 0.60/0.84 inference(modus_ponens,[status(thm)],[763, 761])).
% 0.60/0.84 tff(765,plain,
% 0.60/0.84 ((~hskp9) | c2_1(a136)),
% 0.60/0.84 inference(modus_ponens,[status(thm)],[764, 761])).
% 0.60/0.84 tff(766,plain,
% 0.60/0.84 ((~hskp9) | c2_1(a136)),
% 0.60/0.84 inference(modus_ponens,[status(thm)],[765, 761])).
% 0.60/0.84 tff(767,plain,
% 0.60/0.84 ((~hskp9) | c2_1(a136)),
% 0.60/0.84 inference(modus_ponens,[status(thm)],[766, 761])).
% 0.60/0.84 tff(768,plain,
% 0.60/0.84 (c2_1(a136)),
% 0.60/0.84 inference(unit_resolution,[status(thm)],[767, 754])).
% 0.60/0.84 tff(769,plain,
% 0.60/0.84 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp8 | c2_1(a151) | c3_1(a136) | (~ndr1_0) | c1_1(a136) | (~c2_1(a136)) | (~c3_1(a151)) | (~c0_1(a151)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp8 | c2_1(a151) | c3_1(a136) | (~ndr1_0) | c1_1(a136) | (~c2_1(a136)) | (~c3_1(a151)) | (~c0_1(a151)))),
% 0.60/0.84 inference(rewrite,[status(thm)],[])).
% 0.60/0.84 tff(770,plain,
% 0.60/0.84 ((hskp8 | (~ndr1_0) | c2_1(a151) | (~c3_1(a151)) | (~c0_1(a151)) | c3_1(a136) | c1_1(a136) | (~c2_1(a136))) <=> (hskp8 | c2_1(a151) | c3_1(a136) | (~ndr1_0) | c1_1(a136) | (~c2_1(a136)) | (~c3_1(a151)) | (~c0_1(a151)))),
% 0.60/0.84 inference(rewrite,[status(thm)],[])).
% 0.60/0.84 tff(771,plain,
% 0.60/0.84 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp8 | (~ndr1_0) | c2_1(a151) | (~c3_1(a151)) | (~c0_1(a151)) | c3_1(a136) | c1_1(a136) | (~c2_1(a136)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp8 | c2_1(a151) | c3_1(a136) | (~ndr1_0) | c1_1(a136) | (~c2_1(a136)) | (~c3_1(a151)) | (~c0_1(a151))))),
% 0.60/0.84 inference(monotonicity,[status(thm)],[770])).
% 0.60/0.84 tff(772,plain,
% 0.60/0.84 (((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp8 | (~ndr1_0) | c2_1(a151) | (~c3_1(a151)) | (~c0_1(a151)) | c3_1(a136) | c1_1(a136) | (~c2_1(a136)))) <=> ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp8 | c2_1(a151) | c3_1(a136) | (~ndr1_0) | c1_1(a136) | (~c2_1(a136)) | (~c3_1(a151)) | (~c0_1(a151)))),
% 0.60/0.84 inference(transitivity,[status(thm)],[771, 769])).
% 0.60/0.84 tff(773,plain,
% 0.60/0.84 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | (hskp8 | (~ndr1_0) | c2_1(a151) | (~c3_1(a151)) | (~c0_1(a151)) | c3_1(a136) | c1_1(a136) | (~c2_1(a136)))),
% 0.60/0.84 inference(quant_inst,[status(thm)],[])).
% 0.60/0.84 tff(774,plain,
% 0.60/0.84 ((~![V: $i, U: $i] : (hskp8 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c1_1(V) | (~c2_1(V)))) | hskp8 | c2_1(a151) | c3_1(a136) | (~ndr1_0) | c1_1(a136) | (~c2_1(a136)) | (~c3_1(a151)) | (~c0_1(a151))),
% 0.60/0.84 inference(modus_ponens,[status(thm)],[773, 772])).
% 0.60/0.84 tff(775,plain,
% 0.60/0.84 (hskp8 | c1_1(a136)),
% 0.60/0.84 inference(unit_resolution,[status(thm)],[774, 175, 232, 768, 189, 760, 684, 204])).
% 0.60/0.84 tff(776,plain,
% 0.60/0.84 (c1_1(a136)),
% 0.60/0.84 inference(unit_resolution,[status(thm)],[775, 674])).
% 0.60/0.84 tff(777,plain,
% 0.60/0.84 (((~hskp9) | c0_1(a136)) <=> ((~hskp9) | c0_1(a136))),
% 0.60/0.84 inference(rewrite,[status(thm)],[])).
% 0.60/0.84 tff(778,axiom,((~hskp9) | c0_1(a136)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause70')).
% 0.60/0.84 tff(779,plain,
% 0.60/0.84 ((~hskp9) | c0_1(a136)),
% 0.60/0.84 inference(modus_ponens,[status(thm)],[778, 777])).
% 0.60/0.84 tff(780,plain,
% 0.60/0.84 ((~hskp9) | c0_1(a136)),
% 0.60/0.84 inference(modus_ponens,[status(thm)],[779, 777])).
% 0.60/0.84 tff(781,plain,
% 0.60/0.84 ((~hskp9) | c0_1(a136)),
% 0.60/0.84 inference(modus_ponens,[status(thm)],[780, 777])).
% 0.60/0.84 tff(782,plain,
% 0.60/0.84 ((~hskp9) | c0_1(a136)),
% 0.60/0.84 inference(modus_ponens,[status(thm)],[781, 777])).
% 0.60/0.84 tff(783,plain,
% 0.60/0.84 ((~hskp9) | c0_1(a136)),
% 0.60/0.84 inference(modus_ponens,[status(thm)],[782, 777])).
% 0.60/0.84 tff(784,plain,
% 0.60/0.84 (c0_1(a136)),
% 0.60/0.84 inference(unit_resolution,[status(thm)],[783, 754])).
% 0.60/0.84 tff(785,plain,
% 0.60/0.84 (((~![U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp12 | c3_1(a136) | (~ndr1_0) | (~c1_1(a136)) | (~c0_1(a136)))) <=> ((~![U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp12 | c3_1(a136) | (~ndr1_0) | (~c1_1(a136)) | (~c0_1(a136)))),
% 0.60/0.84 inference(rewrite,[status(thm)],[])).
% 0.60/0.84 tff(786,plain,
% 0.60/0.84 ((hskp12 | (~ndr1_0) | c3_1(a136) | (~c1_1(a136)) | (~c0_1(a136))) <=> (hskp12 | c3_1(a136) | (~ndr1_0) | (~c1_1(a136)) | (~c0_1(a136)))),
% 0.60/0.85 inference(rewrite,[status(thm)],[])).
% 0.60/0.85 tff(787,plain,
% 0.60/0.85 (((~![U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp12 | (~ndr1_0) | c3_1(a136) | (~c1_1(a136)) | (~c0_1(a136)))) <=> ((~![U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp12 | c3_1(a136) | (~ndr1_0) | (~c1_1(a136)) | (~c0_1(a136))))),
% 0.60/0.85 inference(monotonicity,[status(thm)],[786])).
% 0.60/0.85 tff(788,plain,
% 0.60/0.85 (((~![U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp12 | (~ndr1_0) | c3_1(a136) | (~c1_1(a136)) | (~c0_1(a136)))) <=> ((~![U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp12 | c3_1(a136) | (~ndr1_0) | (~c1_1(a136)) | (~c0_1(a136)))),
% 0.60/0.85 inference(transitivity,[status(thm)],[787, 785])).
% 0.60/0.85 tff(789,plain,
% 0.60/0.85 ((~![U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp12 | (~ndr1_0) | c3_1(a136) | (~c1_1(a136)) | (~c0_1(a136)))),
% 0.60/0.85 inference(quant_inst,[status(thm)],[])).
% 0.60/0.85 tff(790,plain,
% 0.60/0.85 ((~![U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp12 | c3_1(a136) | (~ndr1_0) | (~c1_1(a136)) | (~c0_1(a136))),
% 0.60/0.85 inference(modus_ponens,[status(thm)],[789, 788])).
% 0.60/0.85 tff(791,plain,
% 0.60/0.85 (hskp12 | (~c1_1(a136))),
% 0.60/0.85 inference(unit_resolution,[status(thm)],[790, 175, 784, 760, 224])).
% 0.60/0.85 tff(792,plain,
% 0.60/0.85 (hskp12),
% 0.60/0.85 inference(unit_resolution,[status(thm)],[791, 776])).
% 0.60/0.85 tff(793,plain,
% 0.60/0.85 (~c0_1(a140)),
% 0.60/0.85 inference(unit_resolution,[status(thm)],[593, 792])).
% 0.60/0.85 tff(794,plain,
% 0.60/0.85 (c3_1(a140)),
% 0.60/0.85 inference(unit_resolution,[status(thm)],[604, 792])).
% 0.60/0.85 tff(795,plain,
% 0.60/0.85 (((~hskp12) | c1_1(a140)) <=> ((~hskp12) | c1_1(a140))),
% 0.60/0.85 inference(rewrite,[status(thm)],[])).
% 0.60/0.85 tff(796,axiom,((~hskp12) | c1_1(a140)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause65')).
% 0.60/0.85 tff(797,plain,
% 0.60/0.85 ((~hskp12) | c1_1(a140)),
% 0.60/0.85 inference(modus_ponens,[status(thm)],[796, 795])).
% 0.60/0.85 tff(798,plain,
% 0.60/0.85 ((~hskp12) | c1_1(a140)),
% 0.60/0.85 inference(modus_ponens,[status(thm)],[797, 795])).
% 0.60/0.85 tff(799,plain,
% 0.60/0.85 ((~hskp12) | c1_1(a140)),
% 0.60/0.85 inference(modus_ponens,[status(thm)],[798, 795])).
% 0.60/0.85 tff(800,plain,
% 0.60/0.85 ((~hskp12) | c1_1(a140)),
% 0.60/0.85 inference(modus_ponens,[status(thm)],[799, 795])).
% 0.60/0.85 tff(801,plain,
% 0.60/0.85 ((~hskp12) | c1_1(a140)),
% 0.60/0.85 inference(modus_ponens,[status(thm)],[800, 795])).
% 0.60/0.85 tff(802,plain,
% 0.60/0.85 (c1_1(a140)),
% 0.60/0.85 inference(unit_resolution,[status(thm)],[801, 792])).
% 0.60/0.85 tff(803,plain,
% 0.60/0.85 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | c0_1(a140) | c0_1(a128) | c3_1(a128) | (~ndr1_0) | (~c1_1(a128)) | (~c3_1(a140)) | (~c1_1(a140)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp6 | c0_1(a140) | c0_1(a128) | c3_1(a128) | (~ndr1_0) | (~c1_1(a128)) | (~c3_1(a140)) | (~c1_1(a140)))),
% 0.60/0.85 inference(rewrite,[status(thm)],[])).
% 0.60/0.85 tff(804,plain,
% 0.60/0.85 ((hskp6 | (~ndr1_0) | c0_1(a140) | (~c3_1(a140)) | (~c1_1(a140)) | c3_1(a128) | c0_1(a128) | (~c1_1(a128))) <=> (hskp6 | c0_1(a140) | c0_1(a128) | c3_1(a128) | (~ndr1_0) | (~c1_1(a128)) | (~c3_1(a140)) | (~c1_1(a140)))),
% 0.60/0.85 inference(rewrite,[status(thm)],[])).
% 0.60/0.85 tff(805,plain,
% 0.60/0.85 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | (~ndr1_0) | c0_1(a140) | (~c3_1(a140)) | (~c1_1(a140)) | c3_1(a128) | c0_1(a128) | (~c1_1(a128)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | c0_1(a140) | c0_1(a128) | c3_1(a128) | (~ndr1_0) | (~c1_1(a128)) | (~c3_1(a140)) | (~c1_1(a140))))),
% 0.60/0.85 inference(monotonicity,[status(thm)],[804])).
% 0.60/0.85 tff(806,plain,
% 0.60/0.85 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | (~ndr1_0) | c0_1(a140) | (~c3_1(a140)) | (~c1_1(a140)) | c3_1(a128) | c0_1(a128) | (~c1_1(a128)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp6 | c0_1(a140) | c0_1(a128) | c3_1(a128) | (~ndr1_0) | (~c1_1(a128)) | (~c3_1(a140)) | (~c1_1(a140)))),
% 0.60/0.85 inference(transitivity,[status(thm)],[805, 803])).
% 0.60/0.85 tff(807,plain,
% 0.60/0.85 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | (~ndr1_0) | c0_1(a140) | (~c3_1(a140)) | (~c1_1(a140)) | c3_1(a128) | c0_1(a128) | (~c1_1(a128)))),
% 0.60/0.85 inference(quant_inst,[status(thm)],[])).
% 0.60/0.85 tff(808,plain,
% 0.60/0.85 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp6 | c0_1(a140) | c0_1(a128) | c3_1(a128) | (~ndr1_0) | (~c1_1(a128)) | (~c3_1(a140)) | (~c1_1(a140))),
% 0.60/0.85 inference(modus_ponens,[status(thm)],[807, 806])).
% 0.60/0.85 tff(809,plain,
% 0.60/0.85 ($false),
% 0.60/0.85 inference(unit_resolution,[status(thm)],[808, 175, 742, 802, 794, 793, 270, 248, 315, 623])).
% 0.60/0.85 tff(810,plain,(hskp1 | c0_1(a128) | c3_1(a128) | hskp18 | hskp21 | (~c0_1(a138)) | (~c3_1(a138)) | c1_1(a138)), inference(lemma,lemma(discharge,[]))).
% 0.60/0.85 tff(811,plain,
% 0.60/0.85 (hskp1),
% 0.60/0.85 inference(unit_resolution,[status(thm)],[810, 270, 248, 95, 53, 141, 140, 139])).
% 0.60/0.85 tff(812,plain,
% 0.60/0.85 (~c3_1(a125)),
% 0.60/0.85 inference(unit_resolution,[status(thm)],[564, 811])).
% 0.60/0.85 tff(813,plain,
% 0.60/0.85 (c1_1(a125)),
% 0.60/0.85 inference(unit_resolution,[status(thm)],[572, 811])).
% 0.60/0.85 tff(814,plain,
% 0.60/0.85 (c0_1(a125)),
% 0.60/0.85 inference(unit_resolution,[status(thm)],[580, 811])).
% 0.60/0.85 tff(815,plain,
% 0.60/0.85 (hskp12),
% 0.60/0.85 inference(unit_resolution,[status(thm)],[587, 175, 814, 813, 812, 224])).
% 0.60/0.85 tff(816,plain,
% 0.60/0.85 (~c0_1(a140)),
% 0.60/0.85 inference(unit_resolution,[status(thm)],[593, 815])).
% 0.60/0.85 tff(817,plain,
% 0.60/0.85 (c3_1(a140)),
% 0.60/0.85 inference(unit_resolution,[status(thm)],[604, 815])).
% 0.60/0.85 tff(818,plain,
% 0.60/0.85 (c1_1(a140)),
% 0.60/0.85 inference(unit_resolution,[status(thm)],[801, 815])).
% 0.60/0.85 tff(819,plain,
% 0.60/0.85 (hskp6),
% 0.60/0.85 inference(unit_resolution,[status(thm)],[808, 175, 818, 817, 816, 270, 248, 315, 623])).
% 0.60/0.85 tff(820,plain,
% 0.60/0.85 (~c2_1(a133)),
% 0.60/0.85 inference(unit_resolution,[status(thm)],[336, 819])).
% 0.60/0.85 tff(821,plain,
% 0.60/0.85 (~c1_1(a133)),
% 0.60/0.85 inference(unit_resolution,[status(thm)],[342, 819])).
% 0.60/0.85 tff(822,plain,
% 0.60/0.85 (~c0_1(a133)),
% 0.60/0.85 inference(unit_resolution,[status(thm)],[348, 819])).
% 0.60/0.85 tff(823,plain,
% 0.60/0.85 (~c2_1(a140)),
% 0.60/0.85 inference(unit_resolution,[status(thm)],[613, 175, 197, 247, 817, 189, 532, 526, 816, 214, 204])).
% 0.60/0.85 tff(824,plain,
% 0.60/0.85 (((~![U: $i] : (hskp14 | hskp3 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp14 | hskp3 | c0_1(a140) | (~ndr1_0) | c2_1(a140) | (~c3_1(a140)))) <=> ((~![U: $i] : (hskp14 | hskp3 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | hskp14 | hskp3 | c0_1(a140) | (~ndr1_0) | c2_1(a140) | (~c3_1(a140)))),
% 0.60/0.85 inference(rewrite,[status(thm)],[])).
% 0.60/0.85 tff(825,plain,
% 0.60/0.85 ((hskp14 | hskp3 | (~ndr1_0) | c0_1(a140) | c2_1(a140) | (~c3_1(a140))) <=> (hskp14 | hskp3 | c0_1(a140) | (~ndr1_0) | c2_1(a140) | (~c3_1(a140)))),
% 0.60/0.85 inference(rewrite,[status(thm)],[])).
% 0.60/0.85 tff(826,plain,
% 0.60/0.85 (((~![U: $i] : (hskp14 | hskp3 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp14 | hskp3 | (~ndr1_0) | c0_1(a140) | c2_1(a140) | (~c3_1(a140)))) <=> ((~![U: $i] : (hskp14 | hskp3 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp14 | hskp3 | c0_1(a140) | (~ndr1_0) | c2_1(a140) | (~c3_1(a140))))),
% 0.60/0.85 inference(monotonicity,[status(thm)],[825])).
% 0.60/0.85 tff(827,plain,
% 0.60/0.85 (((~![U: $i] : (hskp14 | hskp3 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp14 | hskp3 | (~ndr1_0) | c0_1(a140) | c2_1(a140) | (~c3_1(a140)))) <=> ((~![U: $i] : (hskp14 | hskp3 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | hskp14 | hskp3 | c0_1(a140) | (~ndr1_0) | c2_1(a140) | (~c3_1(a140)))),
% 0.60/0.85 inference(transitivity,[status(thm)],[826, 824])).
% 0.60/0.85 tff(828,plain,
% 0.60/0.85 ((~![U: $i] : (hskp14 | hskp3 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp14 | hskp3 | (~ndr1_0) | c0_1(a140) | c2_1(a140) | (~c3_1(a140)))),
% 0.60/0.85 inference(quant_inst,[status(thm)],[])).
% 0.60/0.85 tff(829,plain,
% 0.60/0.85 ((~![U: $i] : (hskp14 | hskp3 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | hskp14 | hskp3 | c0_1(a140) | (~ndr1_0) | c2_1(a140) | (~c3_1(a140))),
% 0.60/0.85 inference(modus_ponens,[status(thm)],[828, 827])).
% 0.60/0.85 tff(830,plain,
% 0.60/0.85 (hskp14 | c2_1(a140)),
% 0.60/0.85 inference(unit_resolution,[status(thm)],[829, 175, 685, 817, 816, 51])).
% 0.60/0.85 tff(831,plain,
% 0.60/0.85 (hskp14),
% 0.60/0.85 inference(unit_resolution,[status(thm)],[830, 823])).
% 0.60/0.85 tff(832,plain,
% 0.60/0.85 (~c3_1(a145)),
% 0.60/0.85 inference(unit_resolution,[status(thm)],[489, 831])).
% 0.60/0.85 tff(833,plain,
% 0.60/0.85 (~c0_1(a145)),
% 0.60/0.85 inference(unit_resolution,[status(thm)],[508, 831])).
% 0.60/0.85 tff(834,plain,
% 0.60/0.85 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a145) | c3_1(a145) | c1_1(a138) | c0_1(a133) | c1_1(a133) | c2_1(a133) | (~ndr1_0) | (~c3_1(a138)) | (~c0_1(a138)) | c2_1(a145))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a145) | c3_1(a145) | c1_1(a138) | c0_1(a133) | c1_1(a133) | c2_1(a133) | (~ndr1_0) | (~c3_1(a138)) | (~c0_1(a138)) | c2_1(a145))),
% 0.60/0.85 inference(rewrite,[status(thm)],[])).
% 0.60/0.85 tff(835,plain,
% 0.60/0.85 (((~ndr1_0) | c1_1(a138) | (~c3_1(a138)) | (~c0_1(a138)) | c3_1(a145) | c0_1(a145) | c2_1(a145) | c2_1(a133) | c1_1(a133) | c0_1(a133)) <=> (c0_1(a145) | c3_1(a145) | c1_1(a138) | c0_1(a133) | c1_1(a133) | c2_1(a133) | (~ndr1_0) | (~c3_1(a138)) | (~c0_1(a138)) | c2_1(a145))),
% 0.60/0.85 inference(rewrite,[status(thm)],[])).
% 0.60/0.85 tff(836,plain,
% 0.60/0.85 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a138) | (~c3_1(a138)) | (~c0_1(a138)) | c3_1(a145) | c0_1(a145) | c2_1(a145) | c2_1(a133) | c1_1(a133) | c0_1(a133))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a145) | c3_1(a145) | c1_1(a138) | c0_1(a133) | c1_1(a133) | c2_1(a133) | (~ndr1_0) | (~c3_1(a138)) | (~c0_1(a138)) | c2_1(a145)))),
% 0.60/0.85 inference(monotonicity,[status(thm)],[835])).
% 0.60/0.85 tff(837,plain,
% 0.60/0.85 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a138) | (~c3_1(a138)) | (~c0_1(a138)) | c3_1(a145) | c0_1(a145) | c2_1(a145) | c2_1(a133) | c1_1(a133) | c0_1(a133))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a145) | c3_1(a145) | c1_1(a138) | c0_1(a133) | c1_1(a133) | c2_1(a133) | (~ndr1_0) | (~c3_1(a138)) | (~c0_1(a138)) | c2_1(a145))),
% 0.60/0.85 inference(transitivity,[status(thm)],[836, 834])).
% 0.60/0.85 tff(838,plain,
% 0.60/0.85 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a138) | (~c3_1(a138)) | (~c0_1(a138)) | c3_1(a145) | c0_1(a145) | c2_1(a145) | c2_1(a133) | c1_1(a133) | c0_1(a133))),
% 0.60/0.85 inference(quant_inst,[status(thm)],[])).
% 0.60/0.85 tff(839,plain,
% 0.60/0.85 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a145) | c3_1(a145) | c1_1(a138) | c0_1(a133) | c1_1(a133) | c2_1(a133) | (~ndr1_0) | (~c3_1(a138)) | (~c0_1(a138)) | c2_1(a145)),
% 0.60/0.85 inference(modus_ponens,[status(thm)],[838, 837])).
% 0.60/0.85 tff(840,plain,
% 0.60/0.85 (c2_1(a145)),
% 0.60/0.85 inference(unit_resolution,[status(thm)],[839, 175, 141, 140, 833, 832, 139, 822, 821, 820, 258])).
% 0.60/0.85 tff(841,plain,
% 0.60/0.85 (~c1_1(a145)),
% 0.60/0.85 inference(unit_resolution,[status(thm)],[495, 831])).
% 0.60/0.85 tff(842,plain,
% 0.60/0.85 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp3 | c1_1(a145) | c3_1(a145) | c0_1(a140) | (~ndr1_0) | c2_1(a140) | (~c3_1(a140)) | (~c2_1(a145)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp3 | c1_1(a145) | c3_1(a145) | c0_1(a140) | (~ndr1_0) | c2_1(a140) | (~c3_1(a140)) | (~c2_1(a145)))),
% 0.60/0.85 inference(rewrite,[status(thm)],[])).
% 0.60/0.85 tff(843,plain,
% 0.60/0.85 ((hskp3 | (~ndr1_0) | c3_1(a145) | c1_1(a145) | (~c2_1(a145)) | c0_1(a140) | c2_1(a140) | (~c3_1(a140))) <=> (hskp3 | c1_1(a145) | c3_1(a145) | c0_1(a140) | (~ndr1_0) | c2_1(a140) | (~c3_1(a140)) | (~c2_1(a145)))),
% 0.60/0.85 inference(rewrite,[status(thm)],[])).
% 0.60/0.85 tff(844,plain,
% 0.60/0.85 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp3 | (~ndr1_0) | c3_1(a145) | c1_1(a145) | (~c2_1(a145)) | c0_1(a140) | c2_1(a140) | (~c3_1(a140)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp3 | c1_1(a145) | c3_1(a145) | c0_1(a140) | (~ndr1_0) | c2_1(a140) | (~c3_1(a140)) | (~c2_1(a145))))),
% 0.60/0.85 inference(monotonicity,[status(thm)],[843])).
% 0.60/0.85 tff(845,plain,
% 0.60/0.85 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp3 | (~ndr1_0) | c3_1(a145) | c1_1(a145) | (~c2_1(a145)) | c0_1(a140) | c2_1(a140) | (~c3_1(a140)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp3 | c1_1(a145) | c3_1(a145) | c0_1(a140) | (~ndr1_0) | c2_1(a140) | (~c3_1(a140)) | (~c2_1(a145)))),
% 0.60/0.85 inference(transitivity,[status(thm)],[844, 842])).
% 0.60/0.85 tff(846,plain,
% 0.60/0.85 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp3 | (~ndr1_0) | c3_1(a145) | c1_1(a145) | (~c2_1(a145)) | c0_1(a140) | c2_1(a140) | (~c3_1(a140)))),
% 0.60/0.85 inference(quant_inst,[status(thm)],[])).
% 0.60/0.85 tff(847,plain,
% 0.60/0.85 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp3 | c1_1(a145) | c3_1(a145) | c0_1(a140) | (~ndr1_0) | c2_1(a140) | (~c3_1(a140)) | (~c2_1(a145))),
% 0.60/0.85 inference(modus_ponens,[status(thm)],[846, 845])).
% 0.60/0.85 tff(848,plain,
% 0.60/0.85 ($false),
% 0.60/0.85 inference(unit_resolution,[status(thm)],[847, 175, 685, 817, 841, 832, 816, 41, 823, 840])).
% 0.60/0.85 tff(849,plain,(c0_1(a128) | (~c0_1(a138)) | (~c3_1(a138)) | c1_1(a138) | c3_1(a128) | hskp18 | hskp21), inference(lemma,lemma(discharge,[]))).
% 0.60/0.85 tff(850,plain,
% 0.60/0.85 (c0_1(a128)),
% 0.60/0.85 inference(unit_resolution,[status(thm)],[849, 53, 140, 139, 248, 95, 141])).
% 0.60/0.85 tff(851,plain,
% 0.60/0.85 (c3_1(a151)),
% 0.60/0.85 inference(unit_resolution,[status(thm)],[203, 175, 53, 95, 607, 597, 128])).
% 0.60/0.85 tff(852,plain,
% 0.60/0.85 (^[V: $i, U: $i] : refl((hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))))),
% 0.60/0.85 inference(bind,[status(th)],[])).
% 0.60/0.85 tff(853,plain,
% 0.60/0.85 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.60/0.85 inference(quant_intro,[status(thm)],[852])).
% 0.60/0.85 tff(854,plain,
% 0.60/0.85 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.60/0.85 inference(rewrite,[status(thm)],[])).
% 0.60/0.85 tff(855,plain,
% 0.60/0.85 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V))))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))), ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | hskp20) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) | hskp20))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V))) | hskp20) <=> (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))), (((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | hskp20) <=> (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))))),
% 0.60/0.85 inference(bind,[status(th)],[])).
% 0.60/0.85 tff(856,plain,
% 0.60/0.85 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | hskp20) <=> ![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.60/0.85 inference(quant_intro,[status(thm)],[855])).
% 0.60/0.85 tff(857,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c2_1(V))) | c2_1(U)) | c1_1(V)) | hskp20)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause173')).
% 0.60/0.85 tff(858,plain,
% 0.60/0.85 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.60/0.85 inference(modus_ponens,[status(thm)],[857, 856])).
% 0.60/0.85 tff(859,plain,
% 0.60/0.85 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.60/0.85 inference(modus_ponens,[status(thm)],[858, 854])).
% 0.60/0.85 tff(860,plain,(
% 0.60/0.85 ![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.60/0.85 inference(skolemize,[status(sab)],[859])).
% 0.60/0.85 tff(861,plain,
% 0.60/0.85 (![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))),
% 0.60/0.85 inference(modus_ponens,[status(thm)],[860, 853])).
% 0.60/0.85 tff(862,plain,
% 0.60/0.85 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp20 | c2_1(a151) | (~c0_1(a128)) | (~c2_1(a128)) | (~ndr1_0) | c1_1(a128) | (~c3_1(a151)) | (~c1_1(a151)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp20 | c2_1(a151) | (~c0_1(a128)) | (~c2_1(a128)) | (~ndr1_0) | c1_1(a128) | (~c3_1(a151)) | (~c1_1(a151)))),
% 0.60/0.85 inference(rewrite,[status(thm)],[])).
% 0.60/0.85 tff(863,plain,
% 0.60/0.85 ((hskp20 | (~ndr1_0) | c2_1(a151) | (~c3_1(a151)) | (~c1_1(a151)) | c1_1(a128) | (~c2_1(a128)) | (~c0_1(a128))) <=> (hskp20 | c2_1(a151) | (~c0_1(a128)) | (~c2_1(a128)) | (~ndr1_0) | c1_1(a128) | (~c3_1(a151)) | (~c1_1(a151)))),
% 0.60/0.85 inference(rewrite,[status(thm)],[])).
% 0.60/0.85 tff(864,plain,
% 0.60/0.85 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | c2_1(a151) | (~c3_1(a151)) | (~c1_1(a151)) | c1_1(a128) | (~c2_1(a128)) | (~c0_1(a128)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp20 | c2_1(a151) | (~c0_1(a128)) | (~c2_1(a128)) | (~ndr1_0) | c1_1(a128) | (~c3_1(a151)) | (~c1_1(a151))))),
% 0.60/0.85 inference(monotonicity,[status(thm)],[863])).
% 0.60/0.85 tff(865,plain,
% 0.60/0.85 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | c2_1(a151) | (~c3_1(a151)) | (~c1_1(a151)) | c1_1(a128) | (~c2_1(a128)) | (~c0_1(a128)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp20 | c2_1(a151) | (~c0_1(a128)) | (~c2_1(a128)) | (~ndr1_0) | c1_1(a128) | (~c3_1(a151)) | (~c1_1(a151)))),
% 0.60/0.85 inference(transitivity,[status(thm)],[864, 862])).
% 0.60/0.85 tff(866,plain,
% 0.60/0.85 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | c2_1(a151) | (~c3_1(a151)) | (~c1_1(a151)) | c1_1(a128) | (~c2_1(a128)) | (~c0_1(a128)))),
% 0.60/0.85 inference(quant_inst,[status(thm)],[])).
% 0.60/0.85 tff(867,plain,
% 0.60/0.85 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp20 | c2_1(a151) | (~c0_1(a128)) | (~c2_1(a128)) | (~ndr1_0) | c1_1(a128) | (~c3_1(a151)) | (~c1_1(a151))),
% 0.60/0.85 inference(modus_ponens,[status(thm)],[866, 865])).
% 0.60/0.85 tff(868,plain,
% 0.60/0.85 (hskp20),
% 0.60/0.85 inference(unit_resolution,[status(thm)],[867, 175, 607, 597, 461, 545, 861, 534, 851])).
% 0.60/0.85 tff(869,plain,
% 0.60/0.85 (((~hskp20) | (~c2_1(a168))) <=> ((~hskp20) | (~c2_1(a168)))),
% 0.60/0.85 inference(rewrite,[status(thm)],[])).
% 0.60/0.85 tff(870,plain,
% 0.60/0.85 (((~c2_1(a168)) | (~hskp20)) <=> ((~hskp20) | (~c2_1(a168)))),
% 0.60/0.85 inference(rewrite,[status(thm)],[])).
% 0.60/0.85 tff(871,axiom,((~c2_1(a168)) | (~hskp20)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause96')).
% 0.60/0.85 tff(872,plain,
% 0.60/0.85 ((~hskp20) | (~c2_1(a168))),
% 0.60/0.85 inference(modus_ponens,[status(thm)],[871, 870])).
% 0.60/0.85 tff(873,plain,
% 0.60/0.85 ((~hskp20) | (~c2_1(a168))),
% 0.60/0.85 inference(modus_ponens,[status(thm)],[872, 869])).
% 0.60/0.85 tff(874,plain,
% 0.60/0.85 (~c2_1(a168)),
% 0.60/0.85 inference(unit_resolution,[status(thm)],[873, 868])).
% 0.60/0.85 tff(875,plain,
% 0.60/0.85 (((~hskp20) | c1_1(a168)) <=> ((~hskp20) | c1_1(a168))),
% 0.60/0.85 inference(rewrite,[status(thm)],[])).
% 0.60/0.85 tff(876,axiom,((~hskp20) | c1_1(a168)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause56')).
% 0.60/0.85 tff(877,plain,
% 0.60/0.85 ((~hskp20) | c1_1(a168)),
% 0.60/0.85 inference(modus_ponens,[status(thm)],[876, 875])).
% 0.60/0.85 tff(878,plain,
% 0.60/0.85 ((~hskp20) | c1_1(a168)),
% 0.60/0.85 inference(modus_ponens,[status(thm)],[877, 875])).
% 0.60/0.85 tff(879,plain,
% 0.60/0.85 ((~hskp20) | c1_1(a168)),
% 0.60/0.85 inference(modus_ponens,[status(thm)],[878, 875])).
% 0.60/0.85 tff(880,plain,
% 0.60/0.85 ((~hskp20) | c1_1(a168)),
% 0.60/0.85 inference(modus_ponens,[status(thm)],[879, 875])).
% 0.60/0.85 tff(881,plain,
% 0.60/0.85 ((~hskp20) | c1_1(a168)),
% 0.60/0.85 inference(modus_ponens,[status(thm)],[880, 875])).
% 0.60/0.85 tff(882,plain,
% 0.60/0.85 (c1_1(a168)),
% 0.60/0.85 inference(unit_resolution,[status(thm)],[881, 868])).
% 0.60/0.85 tff(883,plain,
% 0.60/0.85 (((~![U: $i] : (hskp21 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp21 | hskp18 | c2_1(a168) | (~ndr1_0) | c3_1(a168) | (~c1_1(a168)))) <=> ((~![U: $i] : (hskp21 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | hskp21 | hskp18 | c2_1(a168) | (~ndr1_0) | c3_1(a168) | (~c1_1(a168)))),
% 0.60/0.85 inference(rewrite,[status(thm)],[])).
% 0.60/0.85 tff(884,plain,
% 0.60/0.85 ((hskp21 | hskp18 | (~ndr1_0) | c3_1(a168) | c2_1(a168) | (~c1_1(a168))) <=> (hskp21 | hskp18 | c2_1(a168) | (~ndr1_0) | c3_1(a168) | (~c1_1(a168)))),
% 0.60/0.85 inference(rewrite,[status(thm)],[])).
% 0.60/0.85 tff(885,plain,
% 0.60/0.85 (((~![U: $i] : (hskp21 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp21 | hskp18 | (~ndr1_0) | c3_1(a168) | c2_1(a168) | (~c1_1(a168)))) <=> ((~![U: $i] : (hskp21 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp21 | hskp18 | c2_1(a168) | (~ndr1_0) | c3_1(a168) | (~c1_1(a168))))),
% 0.60/0.85 inference(monotonicity,[status(thm)],[884])).
% 0.60/0.85 tff(886,plain,
% 0.60/0.85 (((~![U: $i] : (hskp21 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp21 | hskp18 | (~ndr1_0) | c3_1(a168) | c2_1(a168) | (~c1_1(a168)))) <=> ((~![U: $i] : (hskp21 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | hskp21 | hskp18 | c2_1(a168) | (~ndr1_0) | c3_1(a168) | (~c1_1(a168)))),
% 0.60/0.85 inference(transitivity,[status(thm)],[885, 883])).
% 0.60/0.85 tff(887,plain,
% 0.60/0.85 ((~![U: $i] : (hskp21 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp21 | hskp18 | (~ndr1_0) | c3_1(a168) | c2_1(a168) | (~c1_1(a168)))),
% 0.60/0.85 inference(quant_inst,[status(thm)],[])).
% 0.60/0.85 tff(888,plain,
% 0.60/0.85 ((~![U: $i] : (hskp21 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | hskp21 | hskp18 | c2_1(a168) | (~ndr1_0) | c3_1(a168) | (~c1_1(a168))),
% 0.60/0.85 inference(modus_ponens,[status(thm)],[887, 886])).
% 0.60/0.85 tff(889,plain,
% 0.60/0.85 (c3_1(a168)),
% 0.60/0.85 inference(unit_resolution,[status(thm)],[888, 175, 53, 95, 882, 874, 128])).
% 0.60/0.85 tff(890,plain,
% 0.60/0.85 (((~hskp20) | (~c0_1(a168))) <=> ((~hskp20) | (~c0_1(a168)))),
% 0.60/0.85 inference(rewrite,[status(thm)],[])).
% 0.60/0.85 tff(891,plain,
% 0.60/0.85 (((~c0_1(a168)) | (~hskp20)) <=> ((~hskp20) | (~c0_1(a168)))),
% 0.60/0.85 inference(rewrite,[status(thm)],[])).
% 0.60/0.85 tff(892,axiom,((~c0_1(a168)) | (~hskp20)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause95')).
% 0.60/0.85 tff(893,plain,
% 0.60/0.85 ((~hskp20) | (~c0_1(a168))),
% 0.60/0.85 inference(modus_ponens,[status(thm)],[892, 891])).
% 0.60/0.85 tff(894,plain,
% 0.60/0.85 ((~hskp20) | (~c0_1(a168))),
% 0.60/0.85 inference(modus_ponens,[status(thm)],[893, 890])).
% 0.60/0.85 tff(895,plain,
% 0.60/0.85 (~c0_1(a168)),
% 0.60/0.85 inference(unit_resolution,[status(thm)],[894, 868])).
% 0.60/0.85 tff(896,plain,
% 0.60/0.85 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp3 | c0_1(a168) | c2_1(a168) | (~c2_1(a128)) | c3_1(a128) | (~ndr1_0) | c1_1(a128) | (~c3_1(a168)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp3 | c0_1(a168) | c2_1(a168) | (~c2_1(a128)) | c3_1(a128) | (~ndr1_0) | c1_1(a128) | (~c3_1(a168)))),
% 0.60/0.85 inference(rewrite,[status(thm)],[])).
% 0.60/0.85 tff(897,plain,
% 0.60/0.85 ((hskp3 | (~ndr1_0) | c3_1(a128) | c1_1(a128) | (~c2_1(a128)) | c0_1(a168) | c2_1(a168) | (~c3_1(a168))) <=> (hskp3 | c0_1(a168) | c2_1(a168) | (~c2_1(a128)) | c3_1(a128) | (~ndr1_0) | c1_1(a128) | (~c3_1(a168)))),
% 0.60/0.85 inference(rewrite,[status(thm)],[])).
% 0.60/0.85 tff(898,plain,
% 0.60/0.85 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp3 | (~ndr1_0) | c3_1(a128) | c1_1(a128) | (~c2_1(a128)) | c0_1(a168) | c2_1(a168) | (~c3_1(a168)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp3 | c0_1(a168) | c2_1(a168) | (~c2_1(a128)) | c3_1(a128) | (~ndr1_0) | c1_1(a128) | (~c3_1(a168))))),
% 0.60/0.85 inference(monotonicity,[status(thm)],[897])).
% 0.60/0.85 tff(899,plain,
% 0.60/0.85 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp3 | (~ndr1_0) | c3_1(a128) | c1_1(a128) | (~c2_1(a128)) | c0_1(a168) | c2_1(a168) | (~c3_1(a168)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp3 | c0_1(a168) | c2_1(a168) | (~c2_1(a128)) | c3_1(a128) | (~ndr1_0) | c1_1(a128) | (~c3_1(a168)))),
% 0.60/0.85 inference(transitivity,[status(thm)],[898, 896])).
% 0.60/0.85 tff(900,plain,
% 0.60/0.85 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp3 | (~ndr1_0) | c3_1(a128) | c1_1(a128) | (~c2_1(a128)) | c0_1(a168) | c2_1(a168) | (~c3_1(a168)))),
% 0.60/0.85 inference(quant_inst,[status(thm)],[])).
% 0.60/0.85 tff(901,plain,
% 0.60/0.85 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp3 | c0_1(a168) | c2_1(a168) | (~c2_1(a128)) | c3_1(a128) | (~ndr1_0) | c1_1(a128) | (~c3_1(a168))),
% 0.60/0.85 inference(modus_ponens,[status(thm)],[900, 899])).
% 0.60/0.85 tff(902,plain,
% 0.60/0.85 ($false),
% 0.60/0.85 inference(unit_resolution,[status(thm)],[901, 175, 551, 895, 874, 545, 248, 41, 534, 889])).
% 0.60/0.85 tff(903,plain,(c1_1(a128) | (~c2_1(a128)) | c3_1(a128) | hskp21 | hskp18 | (~c1_1(a151)) | c2_1(a151) | (~c0_1(a128))), inference(lemma,lemma(discharge,[]))).
% 0.60/0.86 tff(904,plain,
% 0.60/0.86 (c1_1(a128)),
% 0.60/0.86 inference(unit_resolution,[status(thm)],[903, 53, 248, 520, 95, 197, 189, 850])).
% 0.60/0.86 tff(905,plain,
% 0.60/0.86 (((~![U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp12 | (~c0_1(a128)) | c3_1(a128) | (~ndr1_0) | (~c1_1(a128)))) <=> ((~![U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp12 | (~c0_1(a128)) | c3_1(a128) | (~ndr1_0) | (~c1_1(a128)))),
% 0.60/0.86 inference(rewrite,[status(thm)],[])).
% 0.60/0.86 tff(906,plain,
% 0.60/0.86 ((hskp12 | (~ndr1_0) | c3_1(a128) | (~c1_1(a128)) | (~c0_1(a128))) <=> (hskp12 | (~c0_1(a128)) | c3_1(a128) | (~ndr1_0) | (~c1_1(a128)))),
% 0.60/0.86 inference(rewrite,[status(thm)],[])).
% 0.60/0.86 tff(907,plain,
% 0.60/0.86 (((~![U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp12 | (~ndr1_0) | c3_1(a128) | (~c1_1(a128)) | (~c0_1(a128)))) <=> ((~![U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp12 | (~c0_1(a128)) | c3_1(a128) | (~ndr1_0) | (~c1_1(a128))))),
% 0.60/0.86 inference(monotonicity,[status(thm)],[906])).
% 0.60/0.86 tff(908,plain,
% 0.60/0.86 (((~![U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp12 | (~ndr1_0) | c3_1(a128) | (~c1_1(a128)) | (~c0_1(a128)))) <=> ((~![U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp12 | (~c0_1(a128)) | c3_1(a128) | (~ndr1_0) | (~c1_1(a128)))),
% 0.60/0.86 inference(transitivity,[status(thm)],[907, 905])).
% 0.60/0.86 tff(909,plain,
% 0.60/0.86 ((~![U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp12 | (~ndr1_0) | c3_1(a128) | (~c1_1(a128)) | (~c0_1(a128)))),
% 0.60/0.86 inference(quant_inst,[status(thm)],[])).
% 0.60/0.86 tff(910,plain,
% 0.60/0.86 ((~![U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp12 | (~c0_1(a128)) | c3_1(a128) | (~ndr1_0) | (~c1_1(a128))),
% 0.60/0.86 inference(modus_ponens,[status(thm)],[909, 908])).
% 0.60/0.86 tff(911,plain,
% 0.60/0.86 (hskp12 | (~c0_1(a128)) | (~c1_1(a128))),
% 0.60/0.86 inference(unit_resolution,[status(thm)],[910, 175, 248, 224])).
% 0.60/0.86 tff(912,plain,
% 0.60/0.86 (hskp12),
% 0.60/0.86 inference(unit_resolution,[status(thm)],[911, 904, 850])).
% 0.60/0.86 tff(913,plain,
% 0.60/0.86 (~c0_1(a140)),
% 0.60/0.86 inference(unit_resolution,[status(thm)],[593, 912])).
% 0.60/0.86 tff(914,plain,
% 0.60/0.86 (c3_1(a140)),
% 0.60/0.86 inference(unit_resolution,[status(thm)],[604, 912])).
% 0.60/0.86 tff(915,plain,
% 0.60/0.86 (~c2_1(a140)),
% 0.60/0.86 inference(unit_resolution,[status(thm)],[613, 175, 197, 247, 914, 189, 532, 526, 913, 214, 204])).
% 0.60/0.86 tff(916,plain,
% 0.60/0.86 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp13 | (~c0_1(a128)) | (~c2_1(a128)) | c3_1(a128) | (~ndr1_0) | (~c1_1(a128)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp13 | (~c0_1(a128)) | (~c2_1(a128)) | c3_1(a128) | (~ndr1_0) | (~c1_1(a128)))),
% 0.60/0.86 inference(rewrite,[status(thm)],[])).
% 0.60/0.86 tff(917,plain,
% 0.60/0.86 ((hskp13 | (~ndr1_0) | (~c2_1(a128)) | (~c1_1(a128)) | (~c0_1(a128)) | c3_1(a128) | (~c1_1(a128)) | (~c0_1(a128))) <=> (hskp13 | (~c0_1(a128)) | (~c2_1(a128)) | c3_1(a128) | (~ndr1_0) | (~c1_1(a128)))),
% 0.60/0.86 inference(rewrite,[status(thm)],[])).
% 0.60/0.86 tff(918,plain,
% 0.60/0.86 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp13 | (~ndr1_0) | (~c2_1(a128)) | (~c1_1(a128)) | (~c0_1(a128)) | c3_1(a128) | (~c1_1(a128)) | (~c0_1(a128)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp13 | (~c0_1(a128)) | (~c2_1(a128)) | c3_1(a128) | (~ndr1_0) | (~c1_1(a128))))),
% 0.60/0.86 inference(monotonicity,[status(thm)],[917])).
% 0.60/0.86 tff(919,plain,
% 0.60/0.86 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp13 | (~ndr1_0) | (~c2_1(a128)) | (~c1_1(a128)) | (~c0_1(a128)) | c3_1(a128) | (~c1_1(a128)) | (~c0_1(a128)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp13 | (~c0_1(a128)) | (~c2_1(a128)) | c3_1(a128) | (~ndr1_0) | (~c1_1(a128)))),
% 0.71/0.86 inference(transitivity,[status(thm)],[918, 916])).
% 0.71/0.86 tff(920,plain,
% 0.71/0.86 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp13 | (~ndr1_0) | (~c2_1(a128)) | (~c1_1(a128)) | (~c0_1(a128)) | c3_1(a128) | (~c1_1(a128)) | (~c0_1(a128)))),
% 0.71/0.86 inference(quant_inst,[status(thm)],[])).
% 0.71/0.86 tff(921,plain,
% 0.71/0.86 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp13 | (~c0_1(a128)) | (~c2_1(a128)) | c3_1(a128) | (~ndr1_0) | (~c1_1(a128))),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[920, 919])).
% 0.71/0.86 tff(922,plain,
% 0.71/0.86 (hskp13 | (~c0_1(a128)) | (~c1_1(a128))),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[921, 175, 520, 248, 21])).
% 0.71/0.86 tff(923,plain,
% 0.71/0.86 (hskp13),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[922, 904, 850])).
% 0.71/0.86 tff(924,plain,
% 0.71/0.86 (((~hskp13) | (~c3_1(a144))) <=> ((~hskp13) | (~c3_1(a144)))),
% 0.71/0.86 inference(rewrite,[status(thm)],[])).
% 0.71/0.86 tff(925,plain,
% 0.71/0.86 (((~c3_1(a144)) | (~hskp13)) <=> ((~hskp13) | (~c3_1(a144)))),
% 0.71/0.86 inference(rewrite,[status(thm)],[])).
% 0.71/0.86 tff(926,axiom,((~c3_1(a144)) | (~hskp13)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause109')).
% 0.71/0.86 tff(927,plain,
% 0.71/0.86 ((~hskp13) | (~c3_1(a144))),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[926, 925])).
% 0.71/0.86 tff(928,plain,
% 0.71/0.86 ((~hskp13) | (~c3_1(a144))),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[927, 924])).
% 0.71/0.86 tff(929,plain,
% 0.71/0.86 (~c3_1(a144)),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[928, 923])).
% 0.71/0.86 tff(930,plain,
% 0.71/0.86 (((~hskp13) | c2_1(a144)) <=> ((~hskp13) | c2_1(a144))),
% 0.71/0.86 inference(rewrite,[status(thm)],[])).
% 0.71/0.86 tff(931,axiom,((~hskp13) | c2_1(a144)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause64')).
% 0.71/0.86 tff(932,plain,
% 0.71/0.86 ((~hskp13) | c2_1(a144)),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[931, 930])).
% 0.71/0.86 tff(933,plain,
% 0.71/0.86 ((~hskp13) | c2_1(a144)),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[932, 930])).
% 0.71/0.86 tff(934,plain,
% 0.71/0.86 ((~hskp13) | c2_1(a144)),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[933, 930])).
% 0.71/0.86 tff(935,plain,
% 0.71/0.86 ((~hskp13) | c2_1(a144)),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[934, 930])).
% 0.71/0.86 tff(936,plain,
% 0.71/0.86 ((~hskp13) | c2_1(a144)),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[935, 930])).
% 0.71/0.86 tff(937,plain,
% 0.71/0.86 (c2_1(a144)),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[936, 923])).
% 0.71/0.86 tff(938,plain,
% 0.71/0.86 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp3 | c3_1(a144) | c0_1(a140) | (~ndr1_0) | c2_1(a140) | (~c3_1(a140)) | c1_1(a144) | (~c2_1(a144)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp3 | c3_1(a144) | c0_1(a140) | (~ndr1_0) | c2_1(a140) | (~c3_1(a140)) | c1_1(a144) | (~c2_1(a144)))),
% 0.71/0.86 inference(rewrite,[status(thm)],[])).
% 0.71/0.86 tff(939,plain,
% 0.71/0.86 ((hskp3 | (~ndr1_0) | c3_1(a144) | c1_1(a144) | (~c2_1(a144)) | c0_1(a140) | c2_1(a140) | (~c3_1(a140))) <=> (hskp3 | c3_1(a144) | c0_1(a140) | (~ndr1_0) | c2_1(a140) | (~c3_1(a140)) | c1_1(a144) | (~c2_1(a144)))),
% 0.71/0.86 inference(rewrite,[status(thm)],[])).
% 0.71/0.86 tff(940,plain,
% 0.71/0.86 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp3 | (~ndr1_0) | c3_1(a144) | c1_1(a144) | (~c2_1(a144)) | c0_1(a140) | c2_1(a140) | (~c3_1(a140)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp3 | c3_1(a144) | c0_1(a140) | (~ndr1_0) | c2_1(a140) | (~c3_1(a140)) | c1_1(a144) | (~c2_1(a144))))),
% 0.71/0.86 inference(monotonicity,[status(thm)],[939])).
% 0.71/0.86 tff(941,plain,
% 0.71/0.86 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp3 | (~ndr1_0) | c3_1(a144) | c1_1(a144) | (~c2_1(a144)) | c0_1(a140) | c2_1(a140) | (~c3_1(a140)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp3 | c3_1(a144) | c0_1(a140) | (~ndr1_0) | c2_1(a140) | (~c3_1(a140)) | c1_1(a144) | (~c2_1(a144)))),
% 0.71/0.86 inference(transitivity,[status(thm)],[940, 938])).
% 0.71/0.86 tff(942,plain,
% 0.71/0.86 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp3 | (~ndr1_0) | c3_1(a144) | c1_1(a144) | (~c2_1(a144)) | c0_1(a140) | c2_1(a140) | (~c3_1(a140)))),
% 0.71/0.86 inference(quant_inst,[status(thm)],[])).
% 0.71/0.86 tff(943,plain,
% 0.71/0.86 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp3 | c3_1(a144) | c0_1(a140) | (~ndr1_0) | c2_1(a140) | (~c3_1(a140)) | c1_1(a144) | (~c2_1(a144))),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[942, 941])).
% 0.71/0.86 tff(944,plain,
% 0.71/0.86 (c1_1(a144)),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[943, 175, 685, 937, 914, 929, 913, 41, 915])).
% 0.71/0.86 tff(945,plain,
% 0.71/0.86 (((~hskp13) | (~c0_1(a144))) <=> ((~hskp13) | (~c0_1(a144)))),
% 0.71/0.86 inference(rewrite,[status(thm)],[])).
% 0.71/0.86 tff(946,plain,
% 0.71/0.86 (((~c0_1(a144)) | (~hskp13)) <=> ((~hskp13) | (~c0_1(a144)))),
% 0.71/0.86 inference(rewrite,[status(thm)],[])).
% 0.71/0.86 tff(947,axiom,((~c0_1(a144)) | (~hskp13)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause108')).
% 0.71/0.86 tff(948,plain,
% 0.71/0.86 ((~hskp13) | (~c0_1(a144))),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[947, 946])).
% 0.71/0.86 tff(949,plain,
% 0.71/0.86 ((~hskp13) | (~c0_1(a144))),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[948, 945])).
% 0.71/0.86 tff(950,plain,
% 0.71/0.86 (~c0_1(a144)),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[949, 923])).
% 0.71/0.86 tff(951,plain,
% 0.71/0.86 (c1_1(a140)),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[801, 912])).
% 0.71/0.86 tff(952,plain,
% 0.71/0.86 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | c0_1(a144) | c3_1(a144) | c0_1(a140) | (~ndr1_0) | (~c3_1(a140)) | (~c1_1(a140)) | (~c1_1(a144)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp6 | c0_1(a144) | c3_1(a144) | c0_1(a140) | (~ndr1_0) | (~c3_1(a140)) | (~c1_1(a140)) | (~c1_1(a144)))),
% 0.71/0.86 inference(rewrite,[status(thm)],[])).
% 0.71/0.86 tff(953,plain,
% 0.71/0.86 ((hskp6 | (~ndr1_0) | c0_1(a140) | (~c3_1(a140)) | (~c1_1(a140)) | c3_1(a144) | c0_1(a144) | (~c1_1(a144))) <=> (hskp6 | c0_1(a144) | c3_1(a144) | c0_1(a140) | (~ndr1_0) | (~c3_1(a140)) | (~c1_1(a140)) | (~c1_1(a144)))),
% 0.71/0.86 inference(rewrite,[status(thm)],[])).
% 0.71/0.86 tff(954,plain,
% 0.71/0.86 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | (~ndr1_0) | c0_1(a140) | (~c3_1(a140)) | (~c1_1(a140)) | c3_1(a144) | c0_1(a144) | (~c1_1(a144)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | c0_1(a144) | c3_1(a144) | c0_1(a140) | (~ndr1_0) | (~c3_1(a140)) | (~c1_1(a140)) | (~c1_1(a144))))),
% 0.71/0.86 inference(monotonicity,[status(thm)],[953])).
% 0.71/0.86 tff(955,plain,
% 0.71/0.86 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | (~ndr1_0) | c0_1(a140) | (~c3_1(a140)) | (~c1_1(a140)) | c3_1(a144) | c0_1(a144) | (~c1_1(a144)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp6 | c0_1(a144) | c3_1(a144) | c0_1(a140) | (~ndr1_0) | (~c3_1(a140)) | (~c1_1(a140)) | (~c1_1(a144)))),
% 0.71/0.86 inference(transitivity,[status(thm)],[954, 952])).
% 0.71/0.86 tff(956,plain,
% 0.71/0.86 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | (~ndr1_0) | c0_1(a140) | (~c3_1(a140)) | (~c1_1(a140)) | c3_1(a144) | c0_1(a144) | (~c1_1(a144)))),
% 0.71/0.86 inference(quant_inst,[status(thm)],[])).
% 0.71/0.86 tff(957,plain,
% 0.71/0.86 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp6 | c0_1(a144) | c3_1(a144) | c0_1(a140) | (~ndr1_0) | (~c3_1(a140)) | (~c1_1(a140)) | (~c1_1(a144))),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[956, 955])).
% 0.71/0.86 tff(958,plain,
% 0.71/0.86 (hskp6 | (~c1_1(a144))),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[957, 175, 951, 914, 950, 929, 913, 315])).
% 0.71/0.86 tff(959,plain,
% 0.71/0.86 (hskp6),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[958, 944])).
% 0.71/0.86 tff(960,plain,
% 0.71/0.86 (~c2_1(a133)),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[336, 959])).
% 0.71/0.86 tff(961,plain,
% 0.71/0.86 (~c1_1(a133)),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[342, 959])).
% 0.71/0.86 tff(962,plain,
% 0.71/0.86 (~c0_1(a133)),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[348, 959])).
% 0.71/0.86 tff(963,plain,
% 0.71/0.86 (hskp14),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[829, 175, 685, 914, 913, 51, 915])).
% 0.71/0.86 tff(964,plain,
% 0.71/0.86 (~c3_1(a145)),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[489, 963])).
% 0.71/0.86 tff(965,plain,
% 0.71/0.86 (~c0_1(a145)),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[508, 963])).
% 0.71/0.86 tff(966,plain,
% 0.71/0.86 (c2_1(a145)),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[839, 175, 141, 140, 965, 964, 139, 962, 961, 960, 258])).
% 0.71/0.86 tff(967,plain,
% 0.71/0.86 (^[V: $i, U: $i] : refl((hskp22 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> (hskp22 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V))))),
% 0.71/0.86 inference(bind,[status(th)],[])).
% 0.71/0.86 tff(968,plain,
% 0.71/0.86 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 0.71/0.86 inference(quant_intro,[status(thm)],[967])).
% 0.71/0.86 tff(969,plain,
% 0.71/0.86 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 0.71/0.86 inference(rewrite,[status(thm)],[])).
% 0.71/0.86 tff(970,plain,
% 0.71/0.86 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) <=> ((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | (~c3_1(V)) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(V)) | hskp22) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V))) | hskp22))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V))) | hskp22) <=> (hskp22 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(V)) | hskp22) <=> (hskp22 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))))),
% 0.71/0.86 inference(bind,[status(th)],[])).
% 0.71/0.86 tff(971,plain,
% 0.71/0.86 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(V)) | hskp22) <=> ![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 0.71/0.86 inference(quant_intro,[status(thm)],[970])).
% 0.71/0.86 tff(972,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | c2_1(V)) | hskp22)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause176')).
% 0.71/0.86 tff(973,plain,
% 0.71/0.86 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[972, 971])).
% 0.71/0.86 tff(974,plain,
% 0.71/0.86 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[973, 969])).
% 0.71/0.86 tff(975,plain,(
% 0.71/0.86 ![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 0.71/0.86 inference(skolemize,[status(sab)],[974])).
% 0.71/0.86 tff(976,plain,
% 0.71/0.86 (![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[975, 968])).
% 0.71/0.86 tff(977,plain,
% 0.71/0.86 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp22 | c2_1(a151) | (~c0_1(a128)) | (~c2_1(a128)) | (~ndr1_0) | (~c1_1(a128)) | (~c3_1(a151)) | (~c0_1(a151)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp22 | c2_1(a151) | (~c0_1(a128)) | (~c2_1(a128)) | (~ndr1_0) | (~c1_1(a128)) | (~c3_1(a151)) | (~c0_1(a151)))),
% 0.71/0.86 inference(rewrite,[status(thm)],[])).
% 0.71/0.86 tff(978,plain,
% 0.71/0.86 ((hskp22 | (~ndr1_0) | (~c2_1(a128)) | (~c1_1(a128)) | (~c0_1(a128)) | c2_1(a151) | (~c3_1(a151)) | (~c0_1(a151))) <=> (hskp22 | c2_1(a151) | (~c0_1(a128)) | (~c2_1(a128)) | (~ndr1_0) | (~c1_1(a128)) | (~c3_1(a151)) | (~c0_1(a151)))),
% 0.71/0.86 inference(rewrite,[status(thm)],[])).
% 0.71/0.86 tff(979,plain,
% 0.71/0.86 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | (~c2_1(a128)) | (~c1_1(a128)) | (~c0_1(a128)) | c2_1(a151) | (~c3_1(a151)) | (~c0_1(a151)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp22 | c2_1(a151) | (~c0_1(a128)) | (~c2_1(a128)) | (~ndr1_0) | (~c1_1(a128)) | (~c3_1(a151)) | (~c0_1(a151))))),
% 0.71/0.86 inference(monotonicity,[status(thm)],[978])).
% 0.71/0.86 tff(980,plain,
% 0.71/0.86 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | (~c2_1(a128)) | (~c1_1(a128)) | (~c0_1(a128)) | c2_1(a151) | (~c3_1(a151)) | (~c0_1(a151)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp22 | c2_1(a151) | (~c0_1(a128)) | (~c2_1(a128)) | (~ndr1_0) | (~c1_1(a128)) | (~c3_1(a151)) | (~c0_1(a151)))),
% 0.71/0.86 inference(transitivity,[status(thm)],[979, 977])).
% 0.71/0.86 tff(981,plain,
% 0.71/0.86 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | (~c2_1(a128)) | (~c1_1(a128)) | (~c0_1(a128)) | c2_1(a151) | (~c3_1(a151)) | (~c0_1(a151)))),
% 0.71/0.86 inference(quant_inst,[status(thm)],[])).
% 0.71/0.86 tff(982,plain,
% 0.71/0.86 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp22 | c2_1(a151) | (~c0_1(a128)) | (~c2_1(a128)) | (~ndr1_0) | (~c1_1(a128)) | (~c3_1(a151)) | (~c0_1(a151))),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[981, 980])).
% 0.71/0.86 tff(983,plain,
% 0.71/0.86 (hskp22 | (~c0_1(a128)) | (~c1_1(a128))),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[982, 175, 232, 189, 520, 976, 204])).
% 0.71/0.86 tff(984,plain,
% 0.71/0.86 (hskp22),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[983, 904, 850])).
% 0.71/0.86 tff(985,plain,
% 0.71/0.86 (((~hskp22) | (~c1_1(a179))) <=> ((~hskp22) | (~c1_1(a179)))),
% 0.71/0.86 inference(rewrite,[status(thm)],[])).
% 0.71/0.86 tff(986,plain,
% 0.71/0.86 (((~c1_1(a179)) | (~hskp22)) <=> ((~hskp22) | (~c1_1(a179)))),
% 0.71/0.86 inference(rewrite,[status(thm)],[])).
% 0.71/0.86 tff(987,axiom,((~c1_1(a179)) | (~hskp22)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause92')).
% 0.71/0.86 tff(988,plain,
% 0.71/0.86 ((~hskp22) | (~c1_1(a179))),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[987, 986])).
% 0.71/0.86 tff(989,plain,
% 0.71/0.86 ((~hskp22) | (~c1_1(a179))),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[988, 985])).
% 0.71/0.86 tff(990,plain,
% 0.71/0.86 (~c1_1(a179)),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[989, 984])).
% 0.71/0.86 tff(991,plain,
% 0.71/0.86 (((~hskp22) | c2_1(a179)) <=> ((~hskp22) | c2_1(a179))),
% 0.71/0.86 inference(rewrite,[status(thm)],[])).
% 0.71/0.86 tff(992,axiom,((~hskp22) | c2_1(a179)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause54')).
% 0.71/0.86 tff(993,plain,
% 0.71/0.86 ((~hskp22) | c2_1(a179)),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[992, 991])).
% 0.71/0.86 tff(994,plain,
% 0.71/0.86 ((~hskp22) | c2_1(a179)),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[993, 991])).
% 0.71/0.86 tff(995,plain,
% 0.71/0.86 ((~hskp22) | c2_1(a179)),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[994, 991])).
% 0.71/0.86 tff(996,plain,
% 0.71/0.86 ((~hskp22) | c2_1(a179)),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[995, 991])).
% 0.71/0.86 tff(997,plain,
% 0.71/0.86 ((~hskp22) | c2_1(a179)),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[996, 991])).
% 0.71/0.86 tff(998,plain,
% 0.71/0.86 (c2_1(a179)),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[997, 984])).
% 0.71/0.86 tff(999,plain,
% 0.71/0.86 (((~hskp22) | c0_1(a179)) <=> ((~hskp22) | c0_1(a179))),
% 0.71/0.86 inference(rewrite,[status(thm)],[])).
% 0.71/0.86 tff(1000,axiom,((~hskp22) | c0_1(a179)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause53')).
% 0.71/0.86 tff(1001,plain,
% 0.71/0.86 ((~hskp22) | c0_1(a179)),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[1000, 999])).
% 0.71/0.86 tff(1002,plain,
% 0.71/0.86 ((~hskp22) | c0_1(a179)),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[1001, 999])).
% 0.71/0.86 tff(1003,plain,
% 0.71/0.86 ((~hskp22) | c0_1(a179)),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[1002, 999])).
% 0.71/0.86 tff(1004,plain,
% 0.71/0.86 ((~hskp22) | c0_1(a179)),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[1003, 999])).
% 0.71/0.86 tff(1005,plain,
% 0.71/0.86 ((~hskp22) | c0_1(a179)),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[1004, 999])).
% 0.71/0.86 tff(1006,plain,
% 0.71/0.86 (c0_1(a179)),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[1005, 984])).
% 0.71/0.86 tff(1007,plain,
% 0.71/0.86 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp20 | c1_1(a179) | c2_1(a151) | (~ndr1_0) | (~c3_1(a151)) | (~c1_1(a151)) | (~c2_1(a179)) | (~c0_1(a179)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp20 | c1_1(a179) | c2_1(a151) | (~ndr1_0) | (~c3_1(a151)) | (~c1_1(a151)) | (~c2_1(a179)) | (~c0_1(a179)))),
% 0.71/0.86 inference(rewrite,[status(thm)],[])).
% 0.71/0.86 tff(1008,plain,
% 0.71/0.86 ((hskp20 | (~ndr1_0) | c2_1(a151) | (~c3_1(a151)) | (~c1_1(a151)) | c1_1(a179) | (~c2_1(a179)) | (~c0_1(a179))) <=> (hskp20 | c1_1(a179) | c2_1(a151) | (~ndr1_0) | (~c3_1(a151)) | (~c1_1(a151)) | (~c2_1(a179)) | (~c0_1(a179)))),
% 0.71/0.86 inference(rewrite,[status(thm)],[])).
% 0.71/0.86 tff(1009,plain,
% 0.71/0.86 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | c2_1(a151) | (~c3_1(a151)) | (~c1_1(a151)) | c1_1(a179) | (~c2_1(a179)) | (~c0_1(a179)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp20 | c1_1(a179) | c2_1(a151) | (~ndr1_0) | (~c3_1(a151)) | (~c1_1(a151)) | (~c2_1(a179)) | (~c0_1(a179))))),
% 0.71/0.86 inference(monotonicity,[status(thm)],[1008])).
% 0.71/0.86 tff(1010,plain,
% 0.71/0.86 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | c2_1(a151) | (~c3_1(a151)) | (~c1_1(a151)) | c1_1(a179) | (~c2_1(a179)) | (~c0_1(a179)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp20 | c1_1(a179) | c2_1(a151) | (~ndr1_0) | (~c3_1(a151)) | (~c1_1(a151)) | (~c2_1(a179)) | (~c0_1(a179)))),
% 0.71/0.86 inference(transitivity,[status(thm)],[1009, 1007])).
% 0.71/0.86 tff(1011,plain,
% 0.71/0.86 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | c2_1(a151) | (~c3_1(a151)) | (~c1_1(a151)) | c1_1(a179) | (~c2_1(a179)) | (~c0_1(a179)))),
% 0.71/0.86 inference(quant_inst,[status(thm)],[])).
% 0.71/0.86 tff(1012,plain,
% 0.71/0.86 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp20 | c1_1(a179) | c2_1(a151) | (~ndr1_0) | (~c3_1(a151)) | (~c1_1(a151)) | (~c2_1(a179)) | (~c0_1(a179))),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[1011, 1010])).
% 0.71/0.86 tff(1013,plain,
% 0.71/0.86 (hskp20),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[1012, 175, 1006, 998, 197, 990, 189, 861, 204])).
% 0.71/0.86 tff(1014,plain,
% 0.71/0.86 (~c2_1(a168)),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[873, 1013])).
% 0.71/0.86 tff(1015,plain,
% 0.71/0.86 (c1_1(a168)),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[881, 1013])).
% 0.71/0.86 tff(1016,plain,
% 0.71/0.86 (c3_1(a168)),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[888, 175, 53, 95, 1015, 1014, 128])).
% 0.71/0.86 tff(1017,plain,
% 0.71/0.86 (~c1_1(a145)),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[495, 963])).
% 0.71/0.86 tff(1018,plain,
% 0.71/0.86 (~c0_1(a168)),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[894, 1013])).
% 0.71/0.86 tff(1019,plain,
% 0.71/0.86 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp3 | c0_1(a168) | c2_1(a168) | c1_1(a145) | c3_1(a145) | (~ndr1_0) | (~c2_1(a145)) | (~c3_1(a168)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp3 | c0_1(a168) | c2_1(a168) | c1_1(a145) | c3_1(a145) | (~ndr1_0) | (~c2_1(a145)) | (~c3_1(a168)))),
% 0.71/0.86 inference(rewrite,[status(thm)],[])).
% 0.71/0.86 tff(1020,plain,
% 0.71/0.86 ((hskp3 | (~ndr1_0) | c3_1(a145) | c1_1(a145) | (~c2_1(a145)) | c0_1(a168) | c2_1(a168) | (~c3_1(a168))) <=> (hskp3 | c0_1(a168) | c2_1(a168) | c1_1(a145) | c3_1(a145) | (~ndr1_0) | (~c2_1(a145)) | (~c3_1(a168)))),
% 0.71/0.86 inference(rewrite,[status(thm)],[])).
% 0.71/0.86 tff(1021,plain,
% 0.71/0.86 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp3 | (~ndr1_0) | c3_1(a145) | c1_1(a145) | (~c2_1(a145)) | c0_1(a168) | c2_1(a168) | (~c3_1(a168)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp3 | c0_1(a168) | c2_1(a168) | c1_1(a145) | c3_1(a145) | (~ndr1_0) | (~c2_1(a145)) | (~c3_1(a168))))),
% 0.71/0.86 inference(monotonicity,[status(thm)],[1020])).
% 0.71/0.86 tff(1022,plain,
% 0.71/0.86 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp3 | (~ndr1_0) | c3_1(a145) | c1_1(a145) | (~c2_1(a145)) | c0_1(a168) | c2_1(a168) | (~c3_1(a168)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp3 | c0_1(a168) | c2_1(a168) | c1_1(a145) | c3_1(a145) | (~ndr1_0) | (~c2_1(a145)) | (~c3_1(a168)))),
% 0.71/0.86 inference(transitivity,[status(thm)],[1021, 1019])).
% 0.71/0.86 tff(1023,plain,
% 0.71/0.86 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp3 | (~ndr1_0) | c3_1(a145) | c1_1(a145) | (~c2_1(a145)) | c0_1(a168) | c2_1(a168) | (~c3_1(a168)))),
% 0.71/0.86 inference(quant_inst,[status(thm)],[])).
% 0.71/0.86 tff(1024,plain,
% 0.71/0.86 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp3 | c0_1(a168) | c2_1(a168) | c1_1(a145) | c3_1(a145) | (~ndr1_0) | (~c2_1(a145)) | (~c3_1(a168))),
% 0.71/0.86 inference(modus_ponens,[status(thm)],[1023, 1022])).
% 0.71/0.86 tff(1025,plain,
% 0.71/0.86 ($false),
% 0.71/0.86 inference(unit_resolution,[status(thm)],[1024, 175, 685, 1018, 1014, 1017, 964, 41, 1016, 966])).
% 0.71/0.87 tff(1026,plain,(hskp21 | (~c0_1(a138)) | (~c3_1(a138)) | c1_1(a138) | hskp18 | c3_1(a128)), inference(lemma,lemma(discharge,[]))).
% 0.71/0.87 tff(1027,plain,
% 0.71/0.87 (hskp21),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[1026, 248, 140, 139, 95, 141])).
% 0.71/0.87 tff(1028,plain,
% 0.71/0.87 (~c2_1(a170)),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[291, 1027])).
% 0.71/0.87 tff(1029,plain,
% 0.71/0.87 (~c0_1(a170)),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[297, 1027])).
% 0.71/0.87 tff(1030,plain,
% 0.71/0.87 (c3_1(a170)),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[322, 1027])).
% 0.71/0.87 tff(1031,plain,
% 0.71/0.87 (hskp14),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[482, 175, 685, 1030, 1029, 1028, 51])).
% 0.71/0.87 tff(1032,plain,
% 0.71/0.87 (~c3_1(a145)),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[489, 1031])).
% 0.71/0.87 tff(1033,plain,
% 0.71/0.87 (~c1_1(a145)),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[495, 1031])).
% 0.71/0.87 tff(1034,plain,
% 0.71/0.87 (~c2_1(a145)),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[502, 175, 685, 1030, 1029, 1028, 1033, 1032, 41])).
% 0.71/0.87 tff(1035,plain,
% 0.71/0.87 (~c0_1(a145)),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[508, 1031])).
% 0.71/0.87 tff(1036,plain,
% 0.71/0.87 ($false),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[515, 175, 141, 140, 1035, 1033, 1032, 139, 258, 1034])).
% 0.71/0.87 tff(1037,plain,(c3_1(a128) | (~c0_1(a138)) | (~c3_1(a138)) | c1_1(a138) | hskp18), inference(lemma,lemma(discharge,[]))).
% 0.71/0.87 tff(1038,plain,
% 0.71/0.87 (c3_1(a128)),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[1037, 141, 140, 139, 95])).
% 0.71/0.87 tff(1039,plain,
% 0.71/0.87 (((~hskp3) | (~c3_1(a128))) <=> ((~hskp3) | (~c3_1(a128)))),
% 0.71/0.87 inference(rewrite,[status(thm)],[])).
% 0.71/0.87 tff(1040,plain,
% 0.71/0.87 (((~c3_1(a128)) | (~hskp3)) <=> ((~hskp3) | (~c3_1(a128)))),
% 0.71/0.87 inference(rewrite,[status(thm)],[])).
% 0.71/0.87 tff(1041,axiom,((~c3_1(a128)) | (~hskp3)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause125')).
% 0.71/0.87 tff(1042,plain,
% 0.71/0.87 ((~hskp3) | (~c3_1(a128))),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[1041, 1040])).
% 0.71/0.87 tff(1043,plain,
% 0.71/0.87 ((~hskp3) | (~c3_1(a128))),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[1042, 1039])).
% 0.71/0.87 tff(1044,plain,
% 0.71/0.87 (~hskp3),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[1043, 1038])).
% 0.71/0.87 tff(1045,plain,
% 0.71/0.87 (hskp14 | c0_1(a149)),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[718, 175, 52, 606, 595, 51])).
% 0.71/0.87 tff(1046,plain,
% 0.71/0.87 (c0_1(a149)),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[1045, 724])).
% 0.71/0.87 tff(1047,plain,
% 0.71/0.87 (~hskp6),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[741, 724, 52, 596, 1046, 606])).
% 0.71/0.87 tff(1048,plain,
% 0.71/0.87 (hskp9),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[753, 1047, 53])).
% 0.71/0.87 tff(1049,plain,
% 0.71/0.87 (c0_1(a136)),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[783, 1048])).
% 0.71/0.87 tff(1050,plain,
% 0.71/0.87 (~c3_1(a136)),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[759, 1048])).
% 0.71/0.87 tff(1051,plain,
% 0.71/0.87 (c2_1(a136)),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[767, 1048])).
% 0.71/0.87 tff(1052,assumption,(~c1_1(a136)), introduced(assumption)).
% 0.71/0.87 tff(1053,assumption,(c2_1(a136)), introduced(assumption)).
% 0.71/0.87 tff(1054,assumption,(c0_1(a136)), introduced(assumption)).
% 0.71/0.87 tff(1055,plain,
% 0.71/0.87 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp20 | c2_1(a151) | (~ndr1_0) | c1_1(a136) | (~c0_1(a136)) | (~c2_1(a136)) | (~c3_1(a151)) | (~c1_1(a151)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp20 | c2_1(a151) | (~ndr1_0) | c1_1(a136) | (~c0_1(a136)) | (~c2_1(a136)) | (~c3_1(a151)) | (~c1_1(a151)))),
% 0.71/0.87 inference(rewrite,[status(thm)],[])).
% 0.71/0.87 tff(1056,plain,
% 0.71/0.87 ((hskp20 | (~ndr1_0) | c2_1(a151) | (~c3_1(a151)) | (~c1_1(a151)) | c1_1(a136) | (~c2_1(a136)) | (~c0_1(a136))) <=> (hskp20 | c2_1(a151) | (~ndr1_0) | c1_1(a136) | (~c0_1(a136)) | (~c2_1(a136)) | (~c3_1(a151)) | (~c1_1(a151)))),
% 0.71/0.87 inference(rewrite,[status(thm)],[])).
% 0.71/0.87 tff(1057,plain,
% 0.71/0.87 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | c2_1(a151) | (~c3_1(a151)) | (~c1_1(a151)) | c1_1(a136) | (~c2_1(a136)) | (~c0_1(a136)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp20 | c2_1(a151) | (~ndr1_0) | c1_1(a136) | (~c0_1(a136)) | (~c2_1(a136)) | (~c3_1(a151)) | (~c1_1(a151))))),
% 0.71/0.87 inference(monotonicity,[status(thm)],[1056])).
% 0.71/0.87 tff(1058,plain,
% 0.71/0.87 (((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | c2_1(a151) | (~c3_1(a151)) | (~c1_1(a151)) | c1_1(a136) | (~c2_1(a136)) | (~c0_1(a136)))) <=> ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp20 | c2_1(a151) | (~ndr1_0) | c1_1(a136) | (~c0_1(a136)) | (~c2_1(a136)) | (~c3_1(a151)) | (~c1_1(a151)))),
% 0.71/0.87 inference(transitivity,[status(thm)],[1057, 1055])).
% 0.71/0.87 tff(1059,plain,
% 0.71/0.87 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | (hskp20 | (~ndr1_0) | c2_1(a151) | (~c3_1(a151)) | (~c1_1(a151)) | c1_1(a136) | (~c2_1(a136)) | (~c0_1(a136)))),
% 0.71/0.87 inference(quant_inst,[status(thm)],[])).
% 0.71/0.87 tff(1060,plain,
% 0.71/0.87 ((~![V: $i, U: $i] : (hskp20 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | (~c2_1(V)) | (~c0_1(V)))) | hskp20 | c2_1(a151) | (~ndr1_0) | c1_1(a136) | (~c0_1(a136)) | (~c2_1(a136)) | (~c3_1(a151)) | (~c1_1(a151))),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[1059, 1058])).
% 0.71/0.87 tff(1061,plain,
% 0.71/0.87 (hskp20),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[1060, 175, 607, 1054, 1053, 597, 861, 851, 1052])).
% 0.71/0.87 tff(1062,plain,
% 0.71/0.87 (~c2_1(a168)),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[873, 1061])).
% 0.71/0.87 tff(1063,plain,
% 0.71/0.87 (c1_1(a168)),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[881, 1061])).
% 0.71/0.87 tff(1064,plain,
% 0.71/0.87 (c3_1(a168)),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[888, 175, 53, 95, 1063, 1062, 128])).
% 0.71/0.87 tff(1065,assumption,(~c3_1(a136)), introduced(assumption)).
% 0.71/0.87 tff(1066,plain,
% 0.71/0.87 (~c0_1(a168)),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[894, 1061])).
% 0.71/0.87 tff(1067,plain,
% 0.71/0.87 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp3 | c0_1(a168) | c2_1(a168) | c3_1(a136) | (~ndr1_0) | c1_1(a136) | (~c2_1(a136)) | (~c3_1(a168)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp3 | c0_1(a168) | c2_1(a168) | c3_1(a136) | (~ndr1_0) | c1_1(a136) | (~c2_1(a136)) | (~c3_1(a168)))),
% 0.71/0.87 inference(rewrite,[status(thm)],[])).
% 0.71/0.87 tff(1068,plain,
% 0.71/0.87 ((hskp3 | (~ndr1_0) | c3_1(a136) | c1_1(a136) | (~c2_1(a136)) | c0_1(a168) | c2_1(a168) | (~c3_1(a168))) <=> (hskp3 | c0_1(a168) | c2_1(a168) | c3_1(a136) | (~ndr1_0) | c1_1(a136) | (~c2_1(a136)) | (~c3_1(a168)))),
% 0.71/0.87 inference(rewrite,[status(thm)],[])).
% 0.71/0.87 tff(1069,plain,
% 0.71/0.87 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp3 | (~ndr1_0) | c3_1(a136) | c1_1(a136) | (~c2_1(a136)) | c0_1(a168) | c2_1(a168) | (~c3_1(a168)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp3 | c0_1(a168) | c2_1(a168) | c3_1(a136) | (~ndr1_0) | c1_1(a136) | (~c2_1(a136)) | (~c3_1(a168))))),
% 0.71/0.87 inference(monotonicity,[status(thm)],[1068])).
% 0.71/0.87 tff(1070,plain,
% 0.71/0.87 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp3 | (~ndr1_0) | c3_1(a136) | c1_1(a136) | (~c2_1(a136)) | c0_1(a168) | c2_1(a168) | (~c3_1(a168)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp3 | c0_1(a168) | c2_1(a168) | c3_1(a136) | (~ndr1_0) | c1_1(a136) | (~c2_1(a136)) | (~c3_1(a168)))),
% 0.71/0.87 inference(transitivity,[status(thm)],[1069, 1067])).
% 0.71/0.87 tff(1071,plain,
% 0.71/0.87 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp3 | (~ndr1_0) | c3_1(a136) | c1_1(a136) | (~c2_1(a136)) | c0_1(a168) | c2_1(a168) | (~c3_1(a168)))),
% 0.71/0.87 inference(quant_inst,[status(thm)],[])).
% 0.71/0.87 tff(1072,plain,
% 0.71/0.87 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp3 | c0_1(a168) | c2_1(a168) | c3_1(a136) | (~ndr1_0) | c1_1(a136) | (~c2_1(a136)) | (~c3_1(a168))),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[1071, 1070])).
% 0.71/0.87 tff(1073,plain,
% 0.71/0.87 ($false),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[1072, 175, 52, 1053, 1066, 1062, 1065, 41, 1052, 1064])).
% 0.71/0.87 tff(1074,plain,(c1_1(a136) | hskp3 | (~c2_1(a136)) | c3_1(a136) | hskp21 | hskp18 | (~c1_1(a151)) | (~c0_1(a136)) | c2_1(a151)), inference(lemma,lemma(discharge,[]))).
% 0.71/0.87 tff(1075,plain,
% 0.71/0.87 (c1_1(a136)),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[1074, 1051, 52, 1050, 53, 95, 607, 1049, 597])).
% 0.71/0.87 tff(1076,plain,
% 0.71/0.87 (hskp12 | (~c1_1(a136))),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[790, 175, 1049, 1050, 224])).
% 0.71/0.87 tff(1077,plain,
% 0.71/0.87 (hskp12),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[1076, 1075])).
% 0.71/0.87 tff(1078,plain,
% 0.71/0.87 (~c0_1(a140)),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[593, 1077])).
% 0.71/0.87 tff(1079,plain,
% 0.71/0.87 (c3_1(a140)),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[604, 1077])).
% 0.71/0.87 tff(1080,plain,
% 0.71/0.87 (c2_1(a140)),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[829, 175, 724, 52, 1079, 1078, 51])).
% 0.71/0.87 tff(1081,plain,
% 0.71/0.87 ($false),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[613, 175, 607, 606, 1079, 597, 596, 595, 1078, 214, 851, 1080])).
% 0.71/0.87 tff(1082,plain,(hskp14 | (~c1_1(a151)) | (~c3_1(a149)) | c2_1(a151) | c1_1(a149) | c2_1(a149) | hskp3 | hskp21 | hskp18), inference(lemma,lemma(discharge,[]))).
% 0.71/0.87 tff(1083,plain,
% 0.71/0.87 (hskp14),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[1082, 197, 247, 189, 532, 526, 1044, 53, 95])).
% 0.71/0.87 tff(1084,plain,
% 0.71/0.87 (hskp1),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[711, 1083, 532, 141, 140, 526, 139, 1044, 247])).
% 0.71/0.87 tff(1085,plain,
% 0.71/0.87 (~c3_1(a125)),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[564, 1084])).
% 0.71/0.87 tff(1086,plain,
% 0.71/0.87 (c1_1(a125)),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[572, 1084])).
% 0.71/0.87 tff(1087,plain,
% 0.71/0.87 (c0_1(a125)),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[580, 1084])).
% 0.71/0.87 tff(1088,plain,
% 0.71/0.87 (hskp12),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[587, 175, 1087, 1086, 1085, 224])).
% 0.71/0.87 tff(1089,plain,
% 0.71/0.87 (~c0_1(a140)),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[593, 1088])).
% 0.71/0.87 tff(1090,plain,
% 0.71/0.87 (c3_1(a140)),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[604, 1088])).
% 0.71/0.87 tff(1091,plain,
% 0.71/0.87 (~c2_1(a140)),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[613, 175, 197, 247, 1090, 189, 532, 526, 1089, 214, 204])).
% 0.71/0.87 tff(1092,plain,
% 0.71/0.87 (~c3_1(a145)),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[489, 1083])).
% 0.71/0.87 tff(1093,plain,
% 0.71/0.87 (~c1_1(a145)),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[495, 1083])).
% 0.71/0.87 tff(1094,plain,
% 0.71/0.87 (~c2_1(a145)),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[847, 175, 1044, 1090, 1093, 1092, 1089, 41, 1091])).
% 0.71/0.87 tff(1095,plain,
% 0.71/0.87 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W)))),
% 0.71/0.87 inference(bind,[status(th)],[])).
% 0.71/0.87 tff(1096,plain,
% 0.71/0.87 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))),
% 0.71/0.87 inference(quant_intro,[status(thm)],[1095])).
% 0.71/0.87 tff(1097,plain,
% 0.71/0.87 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))),
% 0.71/0.87 inference(rewrite,[status(thm)],[])).
% 0.71/0.87 tff(1098,plain,
% 0.71/0.87 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))) | c1_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V))) | c1_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | c1_1(W))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | c1_1(W)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(W)) | c2_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | c1_1(W)) | c2_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | c2_1(W) | c1_1(W))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(W)) | c2_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | c2_1(W) | c1_1(W)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(W)) | c2_1(W)) | c3_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | c2_1(W) | c1_1(W)) | c3_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | c2_1(W) | c1_1(W)) | c3_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(W)) | c2_1(W)) | c3_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W)))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(W)) | c2_1(W)) | c3_1(W)) | c0_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W)) | c0_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W)) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(W)) | c2_1(W)) | c3_1(W)) | c0_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W)))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(W)) | c2_1(W)) | c3_1(W)) | c0_1(V)) | c3_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W)) | c3_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W)) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(W)) | c2_1(W)) | c3_1(W)) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))))),
% 0.71/0.87 inference(bind,[status(th)],[])).
% 0.71/0.87 tff(1099,plain,
% 0.71/0.87 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(W)) | c2_1(W)) | c3_1(W)) | c0_1(V)) | c3_1(V)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))),
% 0.71/0.87 inference(quant_intro,[status(thm)],[1098])).
% 0.71/0.87 tff(1100,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c2_1(V))) | c1_1(W)) | c2_1(W)) | c3_1(W)) | c0_1(V)) | c3_1(V))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause180')).
% 0.71/0.87 tff(1101,plain,
% 0.71/0.87 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[1100, 1099])).
% 0.71/0.87 tff(1102,plain,
% 0.71/0.87 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[1101, 1097])).
% 0.71/0.87 tff(1103,plain,(
% 0.71/0.87 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))),
% 0.71/0.87 inference(skolemize,[status(sab)],[1102])).
% 0.71/0.87 tff(1104,plain,
% 0.71/0.87 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[1103, 1096])).
% 0.71/0.87 tff(1105,plain,
% 0.71/0.87 (((~![U: $i] : (hskp21 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp21 | hskp18 | c3_1(a125) | (~ndr1_0) | c2_1(a125) | (~c1_1(a125)))) <=> ((~![U: $i] : (hskp21 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | hskp21 | hskp18 | c3_1(a125) | (~ndr1_0) | c2_1(a125) | (~c1_1(a125)))),
% 0.71/0.87 inference(rewrite,[status(thm)],[])).
% 0.71/0.87 tff(1106,plain,
% 0.71/0.87 ((hskp21 | hskp18 | (~ndr1_0) | c3_1(a125) | c2_1(a125) | (~c1_1(a125))) <=> (hskp21 | hskp18 | c3_1(a125) | (~ndr1_0) | c2_1(a125) | (~c1_1(a125)))),
% 0.71/0.87 inference(rewrite,[status(thm)],[])).
% 0.71/0.87 tff(1107,plain,
% 0.71/0.87 (((~![U: $i] : (hskp21 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp21 | hskp18 | (~ndr1_0) | c3_1(a125) | c2_1(a125) | (~c1_1(a125)))) <=> ((~![U: $i] : (hskp21 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp21 | hskp18 | c3_1(a125) | (~ndr1_0) | c2_1(a125) | (~c1_1(a125))))),
% 0.71/0.87 inference(monotonicity,[status(thm)],[1106])).
% 0.71/0.87 tff(1108,plain,
% 0.71/0.87 (((~![U: $i] : (hskp21 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp21 | hskp18 | (~ndr1_0) | c3_1(a125) | c2_1(a125) | (~c1_1(a125)))) <=> ((~![U: $i] : (hskp21 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | hskp21 | hskp18 | c3_1(a125) | (~ndr1_0) | c2_1(a125) | (~c1_1(a125)))),
% 0.71/0.87 inference(transitivity,[status(thm)],[1107, 1105])).
% 0.71/0.87 tff(1109,plain,
% 0.71/0.87 ((~![U: $i] : (hskp21 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp21 | hskp18 | (~ndr1_0) | c3_1(a125) | c2_1(a125) | (~c1_1(a125)))),
% 0.71/0.87 inference(quant_inst,[status(thm)],[])).
% 0.71/0.87 tff(1110,plain,
% 0.71/0.87 ((~![U: $i] : (hskp21 | hskp18 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)))) | hskp21 | hskp18 | c3_1(a125) | (~ndr1_0) | c2_1(a125) | (~c1_1(a125))),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[1109, 1108])).
% 0.71/0.87 tff(1111,plain,
% 0.71/0.87 (c2_1(a125)),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[1110, 175, 53, 95, 1086, 1085, 128])).
% 0.71/0.87 tff(1112,plain,
% 0.71/0.87 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp13 | c3_1(a125) | (~ndr1_0) | (~c0_1(a125)) | (~c2_1(a125)) | (~c1_1(a125)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp13 | c3_1(a125) | (~ndr1_0) | (~c0_1(a125)) | (~c2_1(a125)) | (~c1_1(a125)))),
% 0.71/0.87 inference(rewrite,[status(thm)],[])).
% 0.71/0.87 tff(1113,plain,
% 0.71/0.87 ((hskp13 | (~ndr1_0) | (~c2_1(a125)) | (~c1_1(a125)) | (~c0_1(a125)) | c3_1(a125) | (~c1_1(a125)) | (~c0_1(a125))) <=> (hskp13 | c3_1(a125) | (~ndr1_0) | (~c0_1(a125)) | (~c2_1(a125)) | (~c1_1(a125)))),
% 0.71/0.87 inference(rewrite,[status(thm)],[])).
% 0.71/0.87 tff(1114,plain,
% 0.71/0.87 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp13 | (~ndr1_0) | (~c2_1(a125)) | (~c1_1(a125)) | (~c0_1(a125)) | c3_1(a125) | (~c1_1(a125)) | (~c0_1(a125)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp13 | c3_1(a125) | (~ndr1_0) | (~c0_1(a125)) | (~c2_1(a125)) | (~c1_1(a125))))),
% 0.71/0.87 inference(monotonicity,[status(thm)],[1113])).
% 0.71/0.87 tff(1115,plain,
% 0.71/0.87 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp13 | (~ndr1_0) | (~c2_1(a125)) | (~c1_1(a125)) | (~c0_1(a125)) | c3_1(a125) | (~c1_1(a125)) | (~c0_1(a125)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp13 | c3_1(a125) | (~ndr1_0) | (~c0_1(a125)) | (~c2_1(a125)) | (~c1_1(a125)))),
% 0.71/0.87 inference(transitivity,[status(thm)],[1114, 1112])).
% 0.71/0.87 tff(1116,plain,
% 0.71/0.87 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp13 | (~ndr1_0) | (~c2_1(a125)) | (~c1_1(a125)) | (~c0_1(a125)) | c3_1(a125) | (~c1_1(a125)) | (~c0_1(a125)))),
% 0.71/0.87 inference(quant_inst,[status(thm)],[])).
% 0.71/0.87 tff(1117,plain,
% 0.71/0.87 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp13 | c3_1(a125) | (~ndr1_0) | (~c0_1(a125)) | (~c2_1(a125)) | (~c1_1(a125))),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[1116, 1115])).
% 0.71/0.87 tff(1118,plain,
% 0.71/0.87 (hskp13),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[1117, 175, 1087, 1086, 1085, 21, 1111])).
% 0.71/0.87 tff(1119,plain,
% 0.71/0.87 (~c3_1(a144)),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[928, 1118])).
% 0.71/0.87 tff(1120,plain,
% 0.71/0.87 (~c0_1(a144)),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[949, 1118])).
% 0.71/0.87 tff(1121,plain,
% 0.71/0.87 (c2_1(a144)),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[936, 1118])).
% 0.71/0.87 tff(1122,plain,
% 0.71/0.87 (^[V: $i, U: $i] : refl((hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)) <=> (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)))),
% 0.71/0.87 inference(bind,[status(th)],[])).
% 0.71/0.87 tff(1123,plain,
% 0.71/0.87 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)) <=> ![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))),
% 0.71/0.87 inference(quant_intro,[status(thm)],[1122])).
% 0.71/0.87 tff(1124,plain,
% 0.71/0.87 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)) <=> ![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))),
% 0.71/0.87 inference(rewrite,[status(thm)],[])).
% 0.71/0.87 tff(1125,plain,
% 0.71/0.87 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U))))), (((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))), (((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U))))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V)))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) <=> (((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V)) | c2_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V)))), ((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c0_1(V) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))), ((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)))), (((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp27) <=> (((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)) | hskp27))), rewrite((((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V)) | hskp27) <=> (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))), (((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp27) <=> (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))))),
% 0.71/0.87 inference(bind,[status(th)],[])).
% 0.71/0.87 tff(1126,plain,
% 0.71/0.87 (![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp27) <=> ![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))),
% 0.71/0.87 inference(quant_intro,[status(thm)],[1125])).
% 0.71/0.87 tff(1127,axiom,(![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | c0_1(V)) | c2_1(V)) | c3_1(V)) | hskp27)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause161')).
% 0.71/0.87 tff(1128,plain,
% 0.71/0.87 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[1127, 1126])).
% 0.71/0.87 tff(1129,plain,
% 0.71/0.87 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[1128, 1124])).
% 0.71/0.87 tff(1130,plain,(
% 0.71/0.87 ![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))),
% 0.71/0.87 inference(skolemize,[status(sab)],[1129])).
% 0.71/0.87 tff(1131,plain,
% 0.71/0.87 (![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[1130, 1123])).
% 0.71/0.87 tff(1132,plain,
% 0.71/0.87 (~c0_1(a145)),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[508, 1083])).
% 0.71/0.87 tff(1133,plain,
% 0.71/0.87 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp27 | c0_1(a145) | c3_1(a145) | c0_1(a140) | (~ndr1_0) | c2_1(a140) | (~c3_1(a140)) | c2_1(a145))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp27 | c0_1(a145) | c3_1(a145) | c0_1(a140) | (~ndr1_0) | c2_1(a140) | (~c3_1(a140)) | c2_1(a145))),
% 0.71/0.87 inference(rewrite,[status(thm)],[])).
% 0.71/0.87 tff(1134,plain,
% 0.71/0.87 ((hskp27 | (~ndr1_0) | c0_1(a140) | c2_1(a140) | (~c3_1(a140)) | c3_1(a145) | c0_1(a145) | c2_1(a145)) <=> (hskp27 | c0_1(a145) | c3_1(a145) | c0_1(a140) | (~ndr1_0) | c2_1(a140) | (~c3_1(a140)) | c2_1(a145))),
% 0.71/0.87 inference(rewrite,[status(thm)],[])).
% 0.71/0.87 tff(1135,plain,
% 0.71/0.87 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp27 | (~ndr1_0) | c0_1(a140) | c2_1(a140) | (~c3_1(a140)) | c3_1(a145) | c0_1(a145) | c2_1(a145))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp27 | c0_1(a145) | c3_1(a145) | c0_1(a140) | (~ndr1_0) | c2_1(a140) | (~c3_1(a140)) | c2_1(a145)))),
% 0.71/0.87 inference(monotonicity,[status(thm)],[1134])).
% 0.71/0.87 tff(1136,plain,
% 0.71/0.87 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp27 | (~ndr1_0) | c0_1(a140) | c2_1(a140) | (~c3_1(a140)) | c3_1(a145) | c0_1(a145) | c2_1(a145))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp27 | c0_1(a145) | c3_1(a145) | c0_1(a140) | (~ndr1_0) | c2_1(a140) | (~c3_1(a140)) | c2_1(a145))),
% 0.71/0.87 inference(transitivity,[status(thm)],[1135, 1133])).
% 0.71/0.87 tff(1137,plain,
% 0.71/0.87 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp27 | (~ndr1_0) | c0_1(a140) | c2_1(a140) | (~c3_1(a140)) | c3_1(a145) | c0_1(a145) | c2_1(a145))),
% 0.71/0.87 inference(quant_inst,[status(thm)],[])).
% 0.71/0.87 tff(1138,plain,
% 0.71/0.87 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp27 | c0_1(a145) | c3_1(a145) | c0_1(a140) | (~ndr1_0) | c2_1(a140) | (~c3_1(a140)) | c2_1(a145)),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[1137, 1136])).
% 0.71/0.87 tff(1139,plain,
% 0.71/0.87 (hskp27),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[1138, 175, 1090, 1132, 1092, 1089, 1131, 1094, 1091])).
% 0.71/0.87 tff(1140,plain,
% 0.71/0.87 (((~hskp27) | c3_1(a137)) <=> ((~hskp27) | c3_1(a137))),
% 0.71/0.87 inference(rewrite,[status(thm)],[])).
% 0.71/0.87 tff(1141,axiom,((~hskp27) | c3_1(a137)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause48')).
% 0.71/0.87 tff(1142,plain,
% 0.71/0.87 ((~hskp27) | c3_1(a137)),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[1141, 1140])).
% 0.71/0.87 tff(1143,plain,
% 0.71/0.87 ((~hskp27) | c3_1(a137)),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[1142, 1140])).
% 0.71/0.87 tff(1144,plain,
% 0.71/0.87 ((~hskp27) | c3_1(a137)),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[1143, 1140])).
% 0.71/0.87 tff(1145,plain,
% 0.71/0.87 ((~hskp27) | c3_1(a137)),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[1144, 1140])).
% 0.71/0.87 tff(1146,plain,
% 0.71/0.87 ((~hskp27) | c3_1(a137)),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[1145, 1140])).
% 0.71/0.87 tff(1147,plain,
% 0.71/0.87 (c3_1(a137)),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[1146, 1139])).
% 0.71/0.87 tff(1148,plain,
% 0.71/0.87 (((~hskp27) | c2_1(a137)) <=> ((~hskp27) | c2_1(a137))),
% 0.71/0.87 inference(rewrite,[status(thm)],[])).
% 0.71/0.87 tff(1149,axiom,((~hskp27) | c2_1(a137)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause47')).
% 0.71/0.87 tff(1150,plain,
% 0.71/0.87 ((~hskp27) | c2_1(a137)),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[1149, 1148])).
% 0.71/0.87 tff(1151,plain,
% 0.71/0.87 ((~hskp27) | c2_1(a137)),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[1150, 1148])).
% 0.71/0.87 tff(1152,plain,
% 0.71/0.87 ((~hskp27) | c2_1(a137)),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[1151, 1148])).
% 0.71/0.87 tff(1153,plain,
% 0.71/0.87 ((~hskp27) | c2_1(a137)),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[1152, 1148])).
% 0.71/0.87 tff(1154,plain,
% 0.71/0.87 ((~hskp27) | c2_1(a137)),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[1153, 1148])).
% 0.71/0.87 tff(1155,plain,
% 0.71/0.87 (c2_1(a137)),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[1154, 1139])).
% 0.71/0.87 tff(1156,plain,
% 0.71/0.87 (((~hskp27) | c1_1(a137)) <=> ((~hskp27) | c1_1(a137))),
% 0.71/0.87 inference(rewrite,[status(thm)],[])).
% 0.71/0.87 tff(1157,axiom,((~hskp27) | c1_1(a137)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause46')).
% 0.71/0.87 tff(1158,plain,
% 0.71/0.87 ((~hskp27) | c1_1(a137)),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[1157, 1156])).
% 0.71/0.87 tff(1159,plain,
% 0.71/0.87 ((~hskp27) | c1_1(a137)),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[1158, 1156])).
% 0.71/0.87 tff(1160,plain,
% 0.71/0.87 ((~hskp27) | c1_1(a137)),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[1159, 1156])).
% 0.71/0.87 tff(1161,plain,
% 0.71/0.87 ((~hskp27) | c1_1(a137)),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[1160, 1156])).
% 0.71/0.87 tff(1162,plain,
% 0.71/0.87 ((~hskp27) | c1_1(a137)),
% 0.71/0.87 inference(modus_ponens,[status(thm)],[1161, 1156])).
% 0.71/0.87 tff(1163,plain,
% 0.71/0.87 (c1_1(a137)),
% 0.71/0.87 inference(unit_resolution,[status(thm)],[1162, 1139])).
% 0.71/0.87 tff(1164,plain,
% 0.71/0.87 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c1_1(a145) | c3_1(a145) | c0_1(a144) | c3_1(a144) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | (~c2_1(a144)) | c2_1(a145))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c1_1(a145) | c3_1(a145) | c0_1(a144) | c3_1(a144) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | (~c2_1(a144)) | c2_1(a145))),
% 0.71/0.87 inference(rewrite,[status(thm)],[])).
% 0.71/0.88 tff(1165,plain,
% 0.71/0.88 (((~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | c3_1(a144) | c0_1(a144) | (~c2_1(a144)) | c2_1(a145) | c1_1(a145) | c3_1(a145)) <=> (c1_1(a145) | c3_1(a145) | c0_1(a144) | c3_1(a144) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | (~c2_1(a144)) | c2_1(a145))),
% 0.71/0.88 inference(rewrite,[status(thm)],[])).
% 0.71/0.88 tff(1166,plain,
% 0.71/0.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | c3_1(a144) | c0_1(a144) | (~c2_1(a144)) | c2_1(a145) | c1_1(a145) | c3_1(a145))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c1_1(a145) | c3_1(a145) | c0_1(a144) | c3_1(a144) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | (~c2_1(a144)) | c2_1(a145)))),
% 0.71/0.88 inference(monotonicity,[status(thm)],[1165])).
% 0.71/0.88 tff(1167,plain,
% 0.71/0.88 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | c3_1(a144) | c0_1(a144) | (~c2_1(a144)) | c2_1(a145) | c1_1(a145) | c3_1(a145))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c1_1(a145) | c3_1(a145) | c0_1(a144) | c3_1(a144) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | (~c2_1(a144)) | c2_1(a145))),
% 0.71/0.88 inference(transitivity,[status(thm)],[1166, 1164])).
% 0.71/0.88 tff(1168,plain,
% 0.71/0.88 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | c3_1(a144) | c0_1(a144) | (~c2_1(a144)) | c2_1(a145) | c1_1(a145) | c3_1(a145))),
% 0.71/0.88 inference(quant_inst,[status(thm)],[])).
% 0.71/0.88 tff(1169,plain,
% 0.71/0.88 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c1_1(a145) | c3_1(a145) | c0_1(a144) | c3_1(a144) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | (~c2_1(a144)) | c2_1(a145)),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[1168, 1167])).
% 0.71/0.88 tff(1170,plain,
% 0.71/0.88 ($false),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[1169, 175, 1163, 1155, 1147, 1121, 1093, 1092, 1120, 1119, 1104, 1094])).
% 0.71/0.88 tff(1171,plain,(hskp21 | hskp18 | (~c0_1(a138)) | (~c3_1(a138)) | c1_1(a138)), inference(lemma,lemma(discharge,[]))).
% 0.71/0.88 tff(1172,plain,
% 0.71/0.88 (hskp21),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[1171, 118, 95, 110, 102])).
% 0.71/0.88 tff(1173,plain,
% 0.71/0.88 (~c2_1(a170)),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[291, 1172])).
% 0.71/0.88 tff(1174,plain,
% 0.71/0.88 (~c0_1(a170)),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[297, 1172])).
% 0.71/0.88 tff(1175,plain,
% 0.71/0.88 (c3_1(a170)),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[322, 1172])).
% 0.71/0.88 tff(1176,plain,
% 0.71/0.88 (c3_1(a128)),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[1037, 118, 110, 102, 95])).
% 0.71/0.88 tff(1177,plain,
% 0.71/0.88 (~hskp3),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[1043, 1176])).
% 0.71/0.88 tff(1178,plain,
% 0.71/0.88 (hskp14),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[482, 175, 1177, 1175, 1174, 1173, 51])).
% 0.71/0.88 tff(1179,plain,
% 0.71/0.88 (~c3_1(a145)),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[489, 1178])).
% 0.71/0.88 tff(1180,plain,
% 0.71/0.88 (~c1_1(a145)),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[495, 1178])).
% 0.71/0.88 tff(1181,plain,
% 0.71/0.88 (~c2_1(a145)),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[502, 175, 1177, 1175, 1174, 1173, 1180, 1179, 41])).
% 0.71/0.88 tff(1182,plain,
% 0.71/0.88 (~c0_1(a145)),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[508, 1178])).
% 0.71/0.88 tff(1183,plain,
% 0.71/0.88 ($false),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[515, 175, 118, 110, 1182, 1180, 1179, 102, 258, 1181])).
% 0.71/0.88 tff(1184,plain,((~hskp10) | hskp18), inference(lemma,lemma(discharge,[]))).
% 0.71/0.88 tff(1185,plain,
% 0.71/0.88 (~hskp10),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[1184, 95])).
% 0.71/0.88 tff(1186,plain,
% 0.71/0.88 (hskp30),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[173, 1185, 95])).
% 0.71/0.88 tff(1187,plain,
% 0.71/0.88 (((~hskp30) | c2_1(a199)) <=> ((~hskp30) | c2_1(a199))),
% 0.71/0.88 inference(rewrite,[status(thm)],[])).
% 0.71/0.88 tff(1188,axiom,((~hskp30) | c2_1(a199)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause39')).
% 0.71/0.88 tff(1189,plain,
% 0.71/0.88 ((~hskp30) | c2_1(a199)),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[1188, 1187])).
% 0.71/0.88 tff(1190,plain,
% 0.71/0.88 ((~hskp30) | c2_1(a199)),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[1189, 1187])).
% 0.71/0.88 tff(1191,plain,
% 0.71/0.88 ((~hskp30) | c2_1(a199)),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[1190, 1187])).
% 0.71/0.88 tff(1192,plain,
% 0.71/0.88 ((~hskp30) | c2_1(a199)),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[1191, 1187])).
% 0.71/0.88 tff(1193,plain,
% 0.71/0.88 ((~hskp30) | c2_1(a199)),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[1192, 1187])).
% 0.71/0.88 tff(1194,plain,
% 0.71/0.88 (c2_1(a199)),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[1193, 1186])).
% 0.71/0.88 tff(1195,plain,
% 0.71/0.88 (((~hskp30) | c1_1(a199)) <=> ((~hskp30) | c1_1(a199))),
% 0.71/0.88 inference(rewrite,[status(thm)],[])).
% 0.71/0.88 tff(1196,axiom,((~hskp30) | c1_1(a199)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause38')).
% 0.71/0.88 tff(1197,plain,
% 0.71/0.88 ((~hskp30) | c1_1(a199)),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[1196, 1195])).
% 0.71/0.88 tff(1198,plain,
% 0.71/0.88 ((~hskp30) | c1_1(a199)),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[1197, 1195])).
% 0.71/0.88 tff(1199,plain,
% 0.71/0.88 ((~hskp30) | c1_1(a199)),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[1198, 1195])).
% 0.71/0.88 tff(1200,plain,
% 0.71/0.88 ((~hskp30) | c1_1(a199)),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[1199, 1195])).
% 0.71/0.88 tff(1201,plain,
% 0.71/0.88 ((~hskp30) | c1_1(a199)),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[1200, 1195])).
% 0.71/0.88 tff(1202,plain,
% 0.71/0.88 (c1_1(a199)),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[1201, 1186])).
% 0.71/0.88 tff(1203,plain,
% 0.71/0.88 (((~hskp30) | c0_1(a199)) <=> ((~hskp30) | c0_1(a199))),
% 0.71/0.88 inference(rewrite,[status(thm)],[])).
% 0.71/0.88 tff(1204,axiom,((~hskp30) | c0_1(a199)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause37')).
% 0.71/0.88 tff(1205,plain,
% 0.71/0.88 ((~hskp30) | c0_1(a199)),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[1204, 1203])).
% 0.71/0.88 tff(1206,plain,
% 0.71/0.88 ((~hskp30) | c0_1(a199)),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[1205, 1203])).
% 0.71/0.88 tff(1207,plain,
% 0.71/0.88 ((~hskp30) | c0_1(a199)),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[1206, 1203])).
% 0.71/0.88 tff(1208,plain,
% 0.71/0.88 ((~hskp30) | c0_1(a199)),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[1207, 1203])).
% 0.71/0.88 tff(1209,plain,
% 0.71/0.88 ((~hskp30) | c0_1(a199)),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[1208, 1203])).
% 0.71/0.88 tff(1210,plain,
% 0.71/0.88 (c0_1(a199)),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[1209, 1186])).
% 0.71/0.88 tff(1211,plain,
% 0.71/0.88 (^[U: $i] : refl((hskp15 | hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) <=> (hskp15 | hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))))),
% 0.71/0.88 inference(bind,[status(th)],[])).
% 0.71/0.88 tff(1212,plain,
% 0.71/0.88 (![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.71/0.88 inference(quant_intro,[status(thm)],[1211])).
% 0.71/0.88 tff(1213,plain,
% 0.71/0.88 (![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.71/0.88 inference(rewrite,[status(thm)],[])).
% 0.71/0.88 tff(1214,plain,
% 0.71/0.88 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) <=> ((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp10) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp10))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp10) <=> (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp10) <=> (hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp10) | hskp15) <=> ((hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp15))), rewrite(((hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp15) <=> (hskp15 | hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp10) | hskp15) <=> (hskp15 | hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))))),
% 0.71/0.88 inference(bind,[status(th)],[])).
% 0.71/0.88 tff(1215,plain,
% 0.71/0.88 (![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp10) | hskp15) <=> ![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.71/0.88 inference(quant_intro,[status(thm)],[1214])).
% 0.71/0.88 tff(1216,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp10) | hskp15)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause155')).
% 0.71/0.88 tff(1217,plain,
% 0.71/0.88 (![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[1216, 1215])).
% 0.71/0.88 tff(1218,plain,
% 0.71/0.88 (![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[1217, 1213])).
% 0.71/0.88 tff(1219,plain,(
% 0.71/0.88 ![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.71/0.88 inference(skolemize,[status(sab)],[1218])).
% 0.71/0.88 tff(1220,plain,
% 0.71/0.88 (![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[1219, 1212])).
% 0.71/0.88 tff(1221,assumption,(c1_1(a199)), introduced(assumption)).
% 0.71/0.88 tff(1222,assumption,(c0_1(a199)), introduced(assumption)).
% 0.71/0.88 tff(1223,assumption,(~hskp10), introduced(assumption)).
% 0.71/0.88 tff(1224,plain,
% 0.71/0.88 (((~![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp15 | hskp10 | (~ndr1_0) | (~c0_1(a199)) | (~c3_1(a199)) | (~c1_1(a199)))) <=> ((~![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp15 | hskp10 | (~ndr1_0) | (~c0_1(a199)) | (~c3_1(a199)) | (~c1_1(a199)))),
% 0.71/0.88 inference(rewrite,[status(thm)],[])).
% 0.71/0.88 tff(1225,plain,
% 0.71/0.88 ((hskp15 | hskp10 | (~ndr1_0) | (~c3_1(a199)) | (~c1_1(a199)) | (~c0_1(a199))) <=> (hskp15 | hskp10 | (~ndr1_0) | (~c0_1(a199)) | (~c3_1(a199)) | (~c1_1(a199)))),
% 0.71/0.88 inference(rewrite,[status(thm)],[])).
% 0.71/0.88 tff(1226,plain,
% 0.71/0.88 (((~![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp15 | hskp10 | (~ndr1_0) | (~c3_1(a199)) | (~c1_1(a199)) | (~c0_1(a199)))) <=> ((~![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp15 | hskp10 | (~ndr1_0) | (~c0_1(a199)) | (~c3_1(a199)) | (~c1_1(a199))))),
% 0.71/0.88 inference(monotonicity,[status(thm)],[1225])).
% 0.71/0.88 tff(1227,plain,
% 0.71/0.88 (((~![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp15 | hskp10 | (~ndr1_0) | (~c3_1(a199)) | (~c1_1(a199)) | (~c0_1(a199)))) <=> ((~![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp15 | hskp10 | (~ndr1_0) | (~c0_1(a199)) | (~c3_1(a199)) | (~c1_1(a199)))),
% 0.71/0.88 inference(transitivity,[status(thm)],[1226, 1224])).
% 0.71/0.88 tff(1228,plain,
% 0.71/0.88 ((~![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp15 | hskp10 | (~ndr1_0) | (~c3_1(a199)) | (~c1_1(a199)) | (~c0_1(a199)))),
% 0.71/0.88 inference(quant_inst,[status(thm)],[])).
% 0.71/0.88 tff(1229,plain,
% 0.71/0.88 ((~![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp15 | hskp10 | (~ndr1_0) | (~c0_1(a199)) | (~c3_1(a199)) | (~c1_1(a199))),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[1228, 1227])).
% 0.71/0.88 tff(1230,plain,
% 0.71/0.88 (hskp15 | (~c3_1(a199))),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[1229, 175, 1223, 1222, 1221, 1220])).
% 0.71/0.88 tff(1231,plain,
% 0.71/0.88 (~c3_1(a199)),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[1230, 74])).
% 0.71/0.88 tff(1232,assumption,(c2_1(a199)), introduced(assumption)).
% 0.71/0.88 tff(1233,plain,
% 0.71/0.88 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp13 | (~ndr1_0) | (~c2_1(a199)) | (~c0_1(a199)) | c3_1(a199) | (~c1_1(a199)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp13 | (~ndr1_0) | (~c2_1(a199)) | (~c0_1(a199)) | c3_1(a199) | (~c1_1(a199)))),
% 0.71/0.88 inference(rewrite,[status(thm)],[])).
% 0.71/0.88 tff(1234,plain,
% 0.71/0.88 ((hskp13 | (~ndr1_0) | (~c2_1(a199)) | (~c1_1(a199)) | (~c0_1(a199)) | c3_1(a199) | (~c1_1(a199)) | (~c0_1(a199))) <=> (hskp13 | (~ndr1_0) | (~c2_1(a199)) | (~c0_1(a199)) | c3_1(a199) | (~c1_1(a199)))),
% 0.71/0.88 inference(rewrite,[status(thm)],[])).
% 0.71/0.88 tff(1235,plain,
% 0.71/0.88 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp13 | (~ndr1_0) | (~c2_1(a199)) | (~c1_1(a199)) | (~c0_1(a199)) | c3_1(a199) | (~c1_1(a199)) | (~c0_1(a199)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp13 | (~ndr1_0) | (~c2_1(a199)) | (~c0_1(a199)) | c3_1(a199) | (~c1_1(a199))))),
% 0.71/0.88 inference(monotonicity,[status(thm)],[1234])).
% 0.71/0.88 tff(1236,plain,
% 0.71/0.88 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp13 | (~ndr1_0) | (~c2_1(a199)) | (~c1_1(a199)) | (~c0_1(a199)) | c3_1(a199) | (~c1_1(a199)) | (~c0_1(a199)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp13 | (~ndr1_0) | (~c2_1(a199)) | (~c0_1(a199)) | c3_1(a199) | (~c1_1(a199)))),
% 0.71/0.88 inference(transitivity,[status(thm)],[1235, 1233])).
% 0.71/0.88 tff(1237,plain,
% 0.71/0.88 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp13 | (~ndr1_0) | (~c2_1(a199)) | (~c1_1(a199)) | (~c0_1(a199)) | c3_1(a199) | (~c1_1(a199)) | (~c0_1(a199)))),
% 0.71/0.88 inference(quant_inst,[status(thm)],[])).
% 0.71/0.88 tff(1238,plain,
% 0.71/0.88 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp13 | (~ndr1_0) | (~c2_1(a199)) | (~c0_1(a199)) | c3_1(a199) | (~c1_1(a199))),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[1237, 1236])).
% 0.71/0.88 tff(1239,plain,
% 0.71/0.88 (hskp13),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[1238, 175, 1222, 1221, 1232, 21, 1231])).
% 0.71/0.88 tff(1240,plain,
% 0.71/0.88 (~c3_1(a144)),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[928, 1239])).
% 0.71/0.88 tff(1241,plain,
% 0.71/0.88 (~c0_1(a144)),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[949, 1239])).
% 0.71/0.88 tff(1242,plain,
% 0.71/0.88 (c2_1(a144)),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[936, 1239])).
% 0.71/0.88 tff(1243,plain,
% 0.71/0.88 (((~![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp29 | hskp3 | c0_1(a144) | c3_1(a144) | (~ndr1_0) | (~c2_1(a144)))) <=> ((~![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | hskp29 | hskp3 | c0_1(a144) | c3_1(a144) | (~ndr1_0) | (~c2_1(a144)))),
% 0.71/0.88 inference(rewrite,[status(thm)],[])).
% 0.71/0.88 tff(1244,plain,
% 0.71/0.88 ((hskp29 | hskp3 | (~ndr1_0) | c3_1(a144) | c0_1(a144) | (~c2_1(a144))) <=> (hskp29 | hskp3 | c0_1(a144) | c3_1(a144) | (~ndr1_0) | (~c2_1(a144)))),
% 0.71/0.88 inference(rewrite,[status(thm)],[])).
% 0.71/0.88 tff(1245,plain,
% 0.71/0.88 (((~![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp29 | hskp3 | (~ndr1_0) | c3_1(a144) | c0_1(a144) | (~c2_1(a144)))) <=> ((~![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp29 | hskp3 | c0_1(a144) | c3_1(a144) | (~ndr1_0) | (~c2_1(a144))))),
% 0.71/0.88 inference(monotonicity,[status(thm)],[1244])).
% 0.71/0.88 tff(1246,plain,
% 0.71/0.88 (((~![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp29 | hskp3 | (~ndr1_0) | c3_1(a144) | c0_1(a144) | (~c2_1(a144)))) <=> ((~![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | hskp29 | hskp3 | c0_1(a144) | c3_1(a144) | (~ndr1_0) | (~c2_1(a144)))),
% 0.71/0.88 inference(transitivity,[status(thm)],[1245, 1243])).
% 0.71/0.88 tff(1247,plain,
% 0.71/0.88 ((~![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | (hskp29 | hskp3 | (~ndr1_0) | c3_1(a144) | c0_1(a144) | (~c2_1(a144)))),
% 0.71/0.88 inference(quant_inst,[status(thm)],[])).
% 0.71/0.88 tff(1248,plain,
% 0.71/0.88 ((~![U: $i] : (hskp29 | hskp3 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c2_1(U)))) | hskp29 | hskp3 | c0_1(a144) | c3_1(a144) | (~ndr1_0) | (~c2_1(a144))),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[1247, 1246])).
% 0.71/0.88 tff(1249,plain,
% 0.71/0.88 (hskp29),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[1248, 175, 52, 1242, 1241, 1240, 73])).
% 0.71/0.88 tff(1250,plain,
% 0.71/0.88 (((~hskp29) | c3_1(a150)) <=> ((~hskp29) | c3_1(a150))),
% 0.71/0.88 inference(rewrite,[status(thm)],[])).
% 0.71/0.88 tff(1251,axiom,((~hskp29) | c3_1(a150)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause42')).
% 0.71/0.88 tff(1252,plain,
% 0.71/0.88 ((~hskp29) | c3_1(a150)),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[1251, 1250])).
% 0.71/0.88 tff(1253,plain,
% 0.71/0.88 ((~hskp29) | c3_1(a150)),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[1252, 1250])).
% 0.71/0.88 tff(1254,plain,
% 0.71/0.88 ((~hskp29) | c3_1(a150)),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[1253, 1250])).
% 0.71/0.88 tff(1255,plain,
% 0.71/0.88 ((~hskp29) | c3_1(a150)),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[1254, 1250])).
% 0.71/0.88 tff(1256,plain,
% 0.71/0.88 ((~hskp29) | c3_1(a150)),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[1255, 1250])).
% 0.71/0.88 tff(1257,plain,
% 0.71/0.88 (c3_1(a150)),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[1256, 1249])).
% 0.71/0.88 tff(1258,plain,
% 0.71/0.88 (((~hskp29) | c1_1(a150)) <=> ((~hskp29) | c1_1(a150))),
% 0.71/0.88 inference(rewrite,[status(thm)],[])).
% 0.71/0.88 tff(1259,axiom,((~hskp29) | c1_1(a150)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause41')).
% 0.71/0.88 tff(1260,plain,
% 0.71/0.88 ((~hskp29) | c1_1(a150)),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[1259, 1258])).
% 0.71/0.88 tff(1261,plain,
% 0.71/0.88 ((~hskp29) | c1_1(a150)),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[1260, 1258])).
% 0.71/0.88 tff(1262,plain,
% 0.71/0.88 ((~hskp29) | c1_1(a150)),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[1261, 1258])).
% 0.71/0.88 tff(1263,plain,
% 0.71/0.88 ((~hskp29) | c1_1(a150)),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[1262, 1258])).
% 0.71/0.88 tff(1264,plain,
% 0.71/0.88 ((~hskp29) | c1_1(a150)),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[1263, 1258])).
% 0.71/0.88 tff(1265,plain,
% 0.71/0.88 (c1_1(a150)),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[1264, 1249])).
% 0.71/0.88 tff(1266,plain,
% 0.71/0.88 (((~hskp29) | c0_1(a150)) <=> ((~hskp29) | c0_1(a150))),
% 0.71/0.88 inference(rewrite,[status(thm)],[])).
% 0.71/0.88 tff(1267,axiom,((~hskp29) | c0_1(a150)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause40')).
% 0.71/0.88 tff(1268,plain,
% 0.71/0.88 ((~hskp29) | c0_1(a150)),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[1267, 1266])).
% 0.71/0.88 tff(1269,plain,
% 0.71/0.88 ((~hskp29) | c0_1(a150)),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[1268, 1266])).
% 0.71/0.88 tff(1270,plain,
% 0.71/0.88 ((~hskp29) | c0_1(a150)),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[1269, 1266])).
% 0.71/0.88 tff(1271,plain,
% 0.71/0.88 ((~hskp29) | c0_1(a150)),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[1270, 1266])).
% 0.71/0.88 tff(1272,plain,
% 0.71/0.88 ((~hskp29) | c0_1(a150)),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[1271, 1266])).
% 0.71/0.88 tff(1273,plain,
% 0.71/0.88 (c0_1(a150)),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[1272, 1249])).
% 0.71/0.88 tff(1274,plain,
% 0.71/0.88 (((~![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp15 | hskp10 | (~ndr1_0) | (~c3_1(a150)) | (~c0_1(a150)) | (~c1_1(a150)))) <=> ((~![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp15 | hskp10 | (~ndr1_0) | (~c3_1(a150)) | (~c0_1(a150)) | (~c1_1(a150)))),
% 0.71/0.88 inference(rewrite,[status(thm)],[])).
% 0.71/0.88 tff(1275,plain,
% 0.71/0.88 ((hskp15 | hskp10 | (~ndr1_0) | (~c3_1(a150)) | (~c1_1(a150)) | (~c0_1(a150))) <=> (hskp15 | hskp10 | (~ndr1_0) | (~c3_1(a150)) | (~c0_1(a150)) | (~c1_1(a150)))),
% 0.71/0.88 inference(rewrite,[status(thm)],[])).
% 0.71/0.88 tff(1276,plain,
% 0.71/0.88 (((~![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp15 | hskp10 | (~ndr1_0) | (~c3_1(a150)) | (~c1_1(a150)) | (~c0_1(a150)))) <=> ((~![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp15 | hskp10 | (~ndr1_0) | (~c3_1(a150)) | (~c0_1(a150)) | (~c1_1(a150))))),
% 0.71/0.88 inference(monotonicity,[status(thm)],[1275])).
% 0.71/0.88 tff(1277,plain,
% 0.71/0.88 (((~![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp15 | hskp10 | (~ndr1_0) | (~c3_1(a150)) | (~c1_1(a150)) | (~c0_1(a150)))) <=> ((~![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp15 | hskp10 | (~ndr1_0) | (~c3_1(a150)) | (~c0_1(a150)) | (~c1_1(a150)))),
% 0.71/0.88 inference(transitivity,[status(thm)],[1276, 1274])).
% 0.71/0.88 tff(1278,plain,
% 0.71/0.88 ((~![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp15 | hskp10 | (~ndr1_0) | (~c3_1(a150)) | (~c1_1(a150)) | (~c0_1(a150)))),
% 0.71/0.88 inference(quant_inst,[status(thm)],[])).
% 0.71/0.88 tff(1279,plain,
% 0.71/0.88 ((~![U: $i] : (hskp15 | hskp10 | (~ndr1_0) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp15 | hskp10 | (~ndr1_0) | (~c3_1(a150)) | (~c0_1(a150)) | (~c1_1(a150))),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[1278, 1277])).
% 0.71/0.88 tff(1280,plain,
% 0.71/0.88 ($false),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[1279, 175, 74, 1223, 1273, 1265, 1257, 1220])).
% 0.71/0.88 tff(1281,plain,(hskp15 | hskp10 | hskp3 | (~c0_1(a199)) | (~c1_1(a199)) | (~c2_1(a199))), inference(lemma,lemma(discharge,[]))).
% 0.71/0.88 tff(1282,plain,
% 0.71/0.88 (hskp15),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[1281, 52, 1185, 1210, 1202, 1194])).
% 0.71/0.88 tff(1283,plain,
% 0.71/0.88 (~c2_1(a149)),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[525, 1282])).
% 0.71/0.88 tff(1284,plain,
% 0.71/0.88 (~c1_1(a149)),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[531, 1282])).
% 0.71/0.88 tff(1285,plain,
% 0.71/0.88 (c3_1(a149)),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[246, 1282])).
% 0.71/0.88 tff(1286,plain,
% 0.71/0.88 (hskp14 | c0_1(a149)),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[718, 175, 52, 1285, 1283, 51])).
% 0.71/0.88 tff(1287,plain,
% 0.71/0.88 (c0_1(a149)),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[1286, 724])).
% 0.71/0.88 tff(1288,plain,
% 0.71/0.88 (((~![U: $i] : (hskp21 | hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp21 | hskp16 | c1_1(a149) | (~ndr1_0) | (~c3_1(a149)) | (~c0_1(a149)))) <=> ((~![U: $i] : (hskp21 | hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp21 | hskp16 | c1_1(a149) | (~ndr1_0) | (~c3_1(a149)) | (~c0_1(a149)))),
% 0.71/0.88 inference(rewrite,[status(thm)],[])).
% 0.71/0.88 tff(1289,plain,
% 0.71/0.88 ((hskp21 | hskp16 | (~ndr1_0) | c1_1(a149) | (~c3_1(a149)) | (~c0_1(a149))) <=> (hskp21 | hskp16 | c1_1(a149) | (~ndr1_0) | (~c3_1(a149)) | (~c0_1(a149)))),
% 0.71/0.88 inference(rewrite,[status(thm)],[])).
% 0.71/0.88 tff(1290,plain,
% 0.71/0.88 (((~![U: $i] : (hskp21 | hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp21 | hskp16 | (~ndr1_0) | c1_1(a149) | (~c3_1(a149)) | (~c0_1(a149)))) <=> ((~![U: $i] : (hskp21 | hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp21 | hskp16 | c1_1(a149) | (~ndr1_0) | (~c3_1(a149)) | (~c0_1(a149))))),
% 0.71/0.88 inference(monotonicity,[status(thm)],[1289])).
% 0.71/0.88 tff(1291,plain,
% 0.71/0.88 (((~![U: $i] : (hskp21 | hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp21 | hskp16 | (~ndr1_0) | c1_1(a149) | (~c3_1(a149)) | (~c0_1(a149)))) <=> ((~![U: $i] : (hskp21 | hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp21 | hskp16 | c1_1(a149) | (~ndr1_0) | (~c3_1(a149)) | (~c0_1(a149)))),
% 0.71/0.88 inference(transitivity,[status(thm)],[1290, 1288])).
% 0.71/0.88 tff(1292,plain,
% 0.71/0.88 ((~![U: $i] : (hskp21 | hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp21 | hskp16 | (~ndr1_0) | c1_1(a149) | (~c3_1(a149)) | (~c0_1(a149)))),
% 0.71/0.88 inference(quant_inst,[status(thm)],[])).
% 0.71/0.88 tff(1293,plain,
% 0.71/0.88 ((~![U: $i] : (hskp21 | hskp16 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp21 | hskp16 | c1_1(a149) | (~ndr1_0) | (~c3_1(a149)) | (~c0_1(a149))),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[1292, 1291])).
% 0.71/0.88 tff(1294,plain,
% 0.71/0.88 (hskp21 | hskp16 | (~c0_1(a149))),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[1293, 175, 1285, 1284, 138])).
% 0.71/0.88 tff(1295,plain,
% 0.71/0.88 (hskp16),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[1294, 1287, 53])).
% 0.71/0.88 tff(1296,plain,
% 0.71/0.88 (c1_1(a151)),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[196, 1295])).
% 0.71/0.88 tff(1297,plain,
% 0.71/0.88 (~c2_1(a151)),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[188, 1295])).
% 0.71/0.88 tff(1298,plain,
% 0.71/0.88 ($false),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[1082, 1297, 1296, 1285, 724, 1284, 1283, 52, 53, 95])).
% 0.71/0.88 tff(1299,plain,(hskp14 | hskp3 | hskp21 | hskp18), inference(lemma,lemma(discharge,[]))).
% 0.71/0.88 tff(1300,plain,
% 0.71/0.88 (hskp14),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[1299, 53, 52, 95])).
% 0.71/0.88 tff(1301,plain,
% 0.71/0.88 (~c0_1(a145)),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[508, 1300])).
% 0.71/0.88 tff(1302,plain,
% 0.71/0.88 (~c3_1(a145)),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[489, 1300])).
% 0.71/0.88 tff(1303,plain,
% 0.71/0.88 (~c1_1(a145)),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[495, 1300])).
% 0.71/0.88 tff(1304,assumption,(~c0_1(a149)), introduced(assumption)).
% 0.71/0.88 tff(1305,assumption,(~c3_1(a145)), introduced(assumption)).
% 0.71/0.88 tff(1306,assumption,(~c1_1(a145)), introduced(assumption)).
% 0.71/0.88 tff(1307,plain,
% 0.71/0.88 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp3 | c2_1(a149) | c1_1(a145) | c3_1(a145) | (~ndr1_0) | (~c2_1(a145)) | (~c3_1(a149)) | c0_1(a149))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp3 | c2_1(a149) | c1_1(a145) | c3_1(a145) | (~ndr1_0) | (~c2_1(a145)) | (~c3_1(a149)) | c0_1(a149))),
% 0.71/0.88 inference(rewrite,[status(thm)],[])).
% 0.71/0.88 tff(1308,plain,
% 0.71/0.88 ((hskp3 | (~ndr1_0) | c3_1(a145) | c1_1(a145) | (~c2_1(a145)) | c0_1(a149) | c2_1(a149) | (~c3_1(a149))) <=> (hskp3 | c2_1(a149) | c1_1(a145) | c3_1(a145) | (~ndr1_0) | (~c2_1(a145)) | (~c3_1(a149)) | c0_1(a149))),
% 0.71/0.88 inference(rewrite,[status(thm)],[])).
% 0.71/0.88 tff(1309,plain,
% 0.71/0.88 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp3 | (~ndr1_0) | c3_1(a145) | c1_1(a145) | (~c2_1(a145)) | c0_1(a149) | c2_1(a149) | (~c3_1(a149)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp3 | c2_1(a149) | c1_1(a145) | c3_1(a145) | (~ndr1_0) | (~c2_1(a145)) | (~c3_1(a149)) | c0_1(a149)))),
% 0.71/0.88 inference(monotonicity,[status(thm)],[1308])).
% 0.71/0.88 tff(1310,plain,
% 0.71/0.88 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp3 | (~ndr1_0) | c3_1(a145) | c1_1(a145) | (~c2_1(a145)) | c0_1(a149) | c2_1(a149) | (~c3_1(a149)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp3 | c2_1(a149) | c1_1(a145) | c3_1(a145) | (~ndr1_0) | (~c2_1(a145)) | (~c3_1(a149)) | c0_1(a149))),
% 0.71/0.88 inference(transitivity,[status(thm)],[1309, 1307])).
% 0.71/0.88 tff(1311,plain,
% 0.71/0.88 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp3 | (~ndr1_0) | c3_1(a145) | c1_1(a145) | (~c2_1(a145)) | c0_1(a149) | c2_1(a149) | (~c3_1(a149)))),
% 0.71/0.88 inference(quant_inst,[status(thm)],[])).
% 0.71/0.88 tff(1312,plain,
% 0.71/0.88 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp3 | c2_1(a149) | c1_1(a145) | c3_1(a145) | (~ndr1_0) | (~c2_1(a145)) | (~c3_1(a149)) | c0_1(a149)),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[1311, 1310])).
% 0.71/0.88 tff(1313,plain,
% 0.71/0.88 (~c2_1(a145)),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[1312, 175, 52, 606, 595, 1306, 1305, 41, 1304])).
% 0.71/0.88 tff(1314,assumption,(~c0_1(a145)), introduced(assumption)).
% 0.71/0.88 tff(1315,plain,
% 0.71/0.88 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | c2_1(a149) | c0_1(a145) | c3_1(a145) | (~ndr1_0) | c2_1(a145) | (~c3_1(a149)) | c0_1(a149))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp9 | c2_1(a149) | c0_1(a145) | c3_1(a145) | (~ndr1_0) | c2_1(a145) | (~c3_1(a149)) | c0_1(a149))),
% 0.71/0.88 inference(rewrite,[status(thm)],[])).
% 0.71/0.88 tff(1316,plain,
% 0.71/0.88 ((hskp9 | (~ndr1_0) | c0_1(a149) | c2_1(a149) | (~c3_1(a149)) | c3_1(a145) | c0_1(a145) | c2_1(a145)) <=> (hskp9 | c2_1(a149) | c0_1(a145) | c3_1(a145) | (~ndr1_0) | c2_1(a145) | (~c3_1(a149)) | c0_1(a149))),
% 0.71/0.88 inference(rewrite,[status(thm)],[])).
% 0.71/0.88 tff(1317,plain,
% 0.71/0.88 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | (~ndr1_0) | c0_1(a149) | c2_1(a149) | (~c3_1(a149)) | c3_1(a145) | c0_1(a145) | c2_1(a145))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | c2_1(a149) | c0_1(a145) | c3_1(a145) | (~ndr1_0) | c2_1(a145) | (~c3_1(a149)) | c0_1(a149)))),
% 0.71/0.88 inference(monotonicity,[status(thm)],[1316])).
% 0.71/0.88 tff(1318,plain,
% 0.71/0.88 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | (~ndr1_0) | c0_1(a149) | c2_1(a149) | (~c3_1(a149)) | c3_1(a145) | c0_1(a145) | c2_1(a145))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp9 | c2_1(a149) | c0_1(a145) | c3_1(a145) | (~ndr1_0) | c2_1(a145) | (~c3_1(a149)) | c0_1(a149))),
% 0.71/0.88 inference(transitivity,[status(thm)],[1317, 1315])).
% 0.71/0.88 tff(1319,plain,
% 0.71/0.88 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | (~ndr1_0) | c0_1(a149) | c2_1(a149) | (~c3_1(a149)) | c3_1(a145) | c0_1(a145) | c2_1(a145))),
% 0.71/0.88 inference(quant_inst,[status(thm)],[])).
% 0.71/0.88 tff(1320,plain,
% 0.71/0.88 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp9 | c2_1(a149) | c0_1(a145) | c3_1(a145) | (~ndr1_0) | c2_1(a145) | (~c3_1(a149)) | c0_1(a149)),
% 0.71/0.88 inference(modus_ponens,[status(thm)],[1319, 1318])).
% 0.71/0.88 tff(1321,plain,
% 0.71/0.88 (hskp9),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[1320, 175, 606, 595, 1314, 1305, 31, 1304, 1313])).
% 0.71/0.88 tff(1322,plain,
% 0.71/0.88 (~c3_1(a136)),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[759, 1321])).
% 0.71/0.88 tff(1323,plain,
% 0.71/0.88 (c2_1(a136)),
% 0.71/0.88 inference(unit_resolution,[status(thm)],[767, 1321])).
% 0.71/0.88 tff(1324,plain,
% 0.71/0.88 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp3 | c2_1(a149) | c3_1(a136) | (~ndr1_0) | c1_1(a136) | (~c2_1(a136)) | (~c3_1(a149)) | c0_1(a149))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp3 | c2_1(a149) | c3_1(a136) | (~ndr1_0) | c1_1(a136) | (~c2_1(a136)) | (~c3_1(a149)) | c0_1(a149))),
% 0.71/0.89 inference(rewrite,[status(thm)],[])).
% 0.71/0.89 tff(1325,plain,
% 0.71/0.89 ((hskp3 | (~ndr1_0) | c3_1(a136) | c1_1(a136) | (~c2_1(a136)) | c0_1(a149) | c2_1(a149) | (~c3_1(a149))) <=> (hskp3 | c2_1(a149) | c3_1(a136) | (~ndr1_0) | c1_1(a136) | (~c2_1(a136)) | (~c3_1(a149)) | c0_1(a149))),
% 0.71/0.89 inference(rewrite,[status(thm)],[])).
% 0.71/0.89 tff(1326,plain,
% 0.71/0.89 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp3 | (~ndr1_0) | c3_1(a136) | c1_1(a136) | (~c2_1(a136)) | c0_1(a149) | c2_1(a149) | (~c3_1(a149)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp3 | c2_1(a149) | c3_1(a136) | (~ndr1_0) | c1_1(a136) | (~c2_1(a136)) | (~c3_1(a149)) | c0_1(a149)))),
% 0.71/0.89 inference(monotonicity,[status(thm)],[1325])).
% 0.71/0.89 tff(1327,plain,
% 0.71/0.89 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp3 | (~ndr1_0) | c3_1(a136) | c1_1(a136) | (~c2_1(a136)) | c0_1(a149) | c2_1(a149) | (~c3_1(a149)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp3 | c2_1(a149) | c3_1(a136) | (~ndr1_0) | c1_1(a136) | (~c2_1(a136)) | (~c3_1(a149)) | c0_1(a149))),
% 0.71/0.89 inference(transitivity,[status(thm)],[1326, 1324])).
% 0.71/0.89 tff(1328,plain,
% 0.71/0.89 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp3 | (~ndr1_0) | c3_1(a136) | c1_1(a136) | (~c2_1(a136)) | c0_1(a149) | c2_1(a149) | (~c3_1(a149)))),
% 0.71/0.89 inference(quant_inst,[status(thm)],[])).
% 0.71/0.89 tff(1329,plain,
% 0.71/0.89 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp3 | c2_1(a149) | c3_1(a136) | (~ndr1_0) | c1_1(a136) | (~c2_1(a136)) | (~c3_1(a149)) | c0_1(a149)),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[1328, 1327])).
% 0.71/0.89 tff(1330,plain,
% 0.71/0.89 (c1_1(a136)),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[1329, 175, 52, 606, 1323, 595, 1322, 41, 1304])).
% 0.71/0.89 tff(1331,plain,
% 0.71/0.89 (c0_1(a136)),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[783, 1321])).
% 0.71/0.89 tff(1332,plain,
% 0.71/0.89 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp13 | c3_1(a136) | (~ndr1_0) | (~c1_1(a136)) | (~c0_1(a136)) | (~c2_1(a136)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp13 | c3_1(a136) | (~ndr1_0) | (~c1_1(a136)) | (~c0_1(a136)) | (~c2_1(a136)))),
% 0.71/0.89 inference(rewrite,[status(thm)],[])).
% 0.71/0.89 tff(1333,plain,
% 0.71/0.89 ((hskp13 | (~ndr1_0) | (~c2_1(a136)) | (~c1_1(a136)) | (~c0_1(a136)) | c3_1(a136) | (~c1_1(a136)) | (~c0_1(a136))) <=> (hskp13 | c3_1(a136) | (~ndr1_0) | (~c1_1(a136)) | (~c0_1(a136)) | (~c2_1(a136)))),
% 0.71/0.89 inference(rewrite,[status(thm)],[])).
% 0.71/0.89 tff(1334,plain,
% 0.71/0.89 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp13 | (~ndr1_0) | (~c2_1(a136)) | (~c1_1(a136)) | (~c0_1(a136)) | c3_1(a136) | (~c1_1(a136)) | (~c0_1(a136)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp13 | c3_1(a136) | (~ndr1_0) | (~c1_1(a136)) | (~c0_1(a136)) | (~c2_1(a136))))),
% 0.71/0.89 inference(monotonicity,[status(thm)],[1333])).
% 0.71/0.89 tff(1335,plain,
% 0.71/0.89 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp13 | (~ndr1_0) | (~c2_1(a136)) | (~c1_1(a136)) | (~c0_1(a136)) | c3_1(a136) | (~c1_1(a136)) | (~c0_1(a136)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp13 | c3_1(a136) | (~ndr1_0) | (~c1_1(a136)) | (~c0_1(a136)) | (~c2_1(a136)))),
% 0.71/0.89 inference(transitivity,[status(thm)],[1334, 1332])).
% 0.71/0.89 tff(1336,plain,
% 0.71/0.89 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp13 | (~ndr1_0) | (~c2_1(a136)) | (~c1_1(a136)) | (~c0_1(a136)) | c3_1(a136) | (~c1_1(a136)) | (~c0_1(a136)))),
% 0.71/0.89 inference(quant_inst,[status(thm)],[])).
% 0.71/0.89 tff(1337,plain,
% 0.71/0.89 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp13 | c3_1(a136) | (~ndr1_0) | (~c1_1(a136)) | (~c0_1(a136)) | (~c2_1(a136))),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[1336, 1335])).
% 0.71/0.89 tff(1338,plain,
% 0.71/0.89 (hskp13 | (~c1_1(a136))),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[1337, 175, 1331, 1323, 1322, 21])).
% 0.71/0.89 tff(1339,plain,
% 0.71/0.89 (hskp13),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[1338, 1330])).
% 0.71/0.89 tff(1340,plain,
% 0.71/0.89 (~c3_1(a144)),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[928, 1339])).
% 0.71/0.89 tff(1341,plain,
% 0.71/0.89 (~c0_1(a144)),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[949, 1339])).
% 0.71/0.89 tff(1342,plain,
% 0.71/0.89 (c2_1(a144)),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[936, 1339])).
% 0.71/0.89 tff(1343,plain,
% 0.71/0.89 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp27 | c2_1(a149) | c0_1(a145) | c3_1(a145) | (~ndr1_0) | c2_1(a145) | (~c3_1(a149)) | c0_1(a149))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp27 | c2_1(a149) | c0_1(a145) | c3_1(a145) | (~ndr1_0) | c2_1(a145) | (~c3_1(a149)) | c0_1(a149))),
% 0.71/0.89 inference(rewrite,[status(thm)],[])).
% 0.71/0.89 tff(1344,plain,
% 0.71/0.89 ((hskp27 | (~ndr1_0) | c0_1(a149) | c2_1(a149) | (~c3_1(a149)) | c3_1(a145) | c0_1(a145) | c2_1(a145)) <=> (hskp27 | c2_1(a149) | c0_1(a145) | c3_1(a145) | (~ndr1_0) | c2_1(a145) | (~c3_1(a149)) | c0_1(a149))),
% 0.71/0.89 inference(rewrite,[status(thm)],[])).
% 0.71/0.89 tff(1345,plain,
% 0.71/0.89 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp27 | (~ndr1_0) | c0_1(a149) | c2_1(a149) | (~c3_1(a149)) | c3_1(a145) | c0_1(a145) | c2_1(a145))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp27 | c2_1(a149) | c0_1(a145) | c3_1(a145) | (~ndr1_0) | c2_1(a145) | (~c3_1(a149)) | c0_1(a149)))),
% 0.71/0.89 inference(monotonicity,[status(thm)],[1344])).
% 0.71/0.89 tff(1346,plain,
% 0.71/0.89 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp27 | (~ndr1_0) | c0_1(a149) | c2_1(a149) | (~c3_1(a149)) | c3_1(a145) | c0_1(a145) | c2_1(a145))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp27 | c2_1(a149) | c0_1(a145) | c3_1(a145) | (~ndr1_0) | c2_1(a145) | (~c3_1(a149)) | c0_1(a149))),
% 0.71/0.89 inference(transitivity,[status(thm)],[1345, 1343])).
% 0.71/0.89 tff(1347,plain,
% 0.71/0.89 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp27 | (~ndr1_0) | c0_1(a149) | c2_1(a149) | (~c3_1(a149)) | c3_1(a145) | c0_1(a145) | c2_1(a145))),
% 0.71/0.89 inference(quant_inst,[status(thm)],[])).
% 0.71/0.89 tff(1348,plain,
% 0.71/0.89 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp27 | c2_1(a149) | c0_1(a145) | c3_1(a145) | (~ndr1_0) | c2_1(a145) | (~c3_1(a149)) | c0_1(a149)),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[1347, 1346])).
% 0.71/0.89 tff(1349,plain,
% 0.71/0.89 (hskp27),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[1348, 175, 606, 595, 1314, 1305, 1131, 1304, 1313])).
% 0.71/0.89 tff(1350,plain,
% 0.71/0.89 (c3_1(a137)),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[1146, 1349])).
% 0.71/0.89 tff(1351,plain,
% 0.71/0.89 (c2_1(a137)),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[1154, 1349])).
% 0.71/0.89 tff(1352,plain,
% 0.71/0.89 (c1_1(a137)),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[1162, 1349])).
% 0.71/0.89 tff(1353,plain,
% 0.71/0.89 ($false),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[1169, 175, 1352, 1351, 1350, 1342, 1306, 1305, 1341, 1340, 1104, 1313])).
% 0.71/0.89 tff(1354,plain,(c0_1(a149) | c1_1(a145) | c3_1(a145) | hskp3 | (~c3_1(a149)) | c2_1(a149) | c0_1(a145)), inference(lemma,lemma(discharge,[]))).
% 0.71/0.89 tff(1355,plain,
% 0.71/0.89 (c0_1(a149)),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[1354, 1303, 1302, 52, 1285, 1283, 1301])).
% 0.71/0.89 tff(1356,plain,
% 0.71/0.89 (hskp16),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[1294, 1355, 53])).
% 0.71/0.89 tff(1357,plain,
% 0.71/0.89 (~c2_1(a151)),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[188, 1356])).
% 0.71/0.89 tff(1358,plain,
% 0.71/0.89 (c1_1(a151)),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[196, 1356])).
% 0.71/0.89 tff(1359,plain,
% 0.71/0.89 (c3_1(a151)),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[203, 175, 53, 95, 1358, 1357, 128])).
% 0.71/0.89 tff(1360,plain,
% 0.71/0.89 (^[W: $i, V: $i, U: $i] : refl(((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W))))),
% 0.71/0.89 inference(bind,[status(th)],[])).
% 0.71/0.89 tff(1361,plain,
% 0.71/0.89 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))),
% 0.71/0.89 inference(quant_intro,[status(thm)],[1360])).
% 0.71/0.89 tff(1362,plain,
% 0.71/0.89 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W))) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))),
% 0.71/0.89 inference(rewrite,[status(thm)],[])).
% 0.71/0.89 tff(1363,plain,
% 0.71/0.89 (^[W: $i, V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c3_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V))))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c0_1(W))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V))) | (~c0_1(W))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c0_1(W)))), ((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c0_1(W))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c0_1(W))))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c0_1(W))) | c2_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c0_1(W))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | (~c3_1(V)) | (~c0_1(V)) | (~c0_1(W))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c0_1(W)))), (((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c0_1(W))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c0_1(W))))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c0_1(W))) | c2_1(V)) | c1_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c0_1(W))) | c1_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | (~c0_1(W))) | c1_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W)))), ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c0_1(W))) | c2_1(V)) | c1_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W))))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c0_1(W))) | c2_1(V)) | c1_1(W)) | c3_1(W)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W))) | c3_1(W)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | (~c0_1(W))) | c3_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))), (((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c0_1(W))) | c2_1(V)) | c1_1(W)) | c3_1(W)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))))),
% 0.71/0.89 inference(bind,[status(th)],[])).
% 0.71/0.89 tff(1364,plain,
% 0.71/0.89 (![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c0_1(W))) | c2_1(V)) | c1_1(W)) | c3_1(W)) <=> ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))),
% 0.71/0.89 inference(quant_intro,[status(thm)],[1363])).
% 0.71/0.89 tff(1365,axiom,(![W: $i, V: $i, U: $i] : ((((((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | (~c3_1(V))) | (~c0_1(W))) | c2_1(V)) | c1_1(W)) | c3_1(W))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause183')).
% 0.71/0.89 tff(1366,plain,
% 0.71/0.89 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[1365, 1364])).
% 0.71/0.89 tff(1367,plain,
% 0.71/0.89 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[1366, 1362])).
% 0.71/0.89 tff(1368,plain,(
% 0.71/0.89 ![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))),
% 0.71/0.89 inference(skolemize,[status(sab)],[1367])).
% 0.71/0.89 tff(1369,plain,
% 0.71/0.89 (![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[1368, 1361])).
% 0.71/0.89 tff(1370,plain,
% 0.71/0.89 (^[U: $i] : refl((hskp11 | hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))) <=> (hskp11 | hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))))),
% 0.71/0.89 inference(bind,[status(th)],[])).
% 0.71/0.89 tff(1371,plain,
% 0.71/0.89 (![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))),
% 0.71/0.89 inference(quant_intro,[status(thm)],[1370])).
% 0.71/0.89 tff(1372,plain,
% 0.71/0.89 (![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))),
% 0.71/0.89 inference(rewrite,[status(thm)],[])).
% 0.71/0.89 tff(1373,plain,
% 0.71/0.89 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c1_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U))))), (((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))), (((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))))), ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp10) <=> (((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))) | hskp10))), rewrite((((~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))) | hskp10) <=> (hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))), ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp10) <=> (hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))))), (((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp10) | hskp11) <=> ((hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))) | hskp11))), rewrite(((hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U))) | hskp11) <=> (hskp11 | hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))), (((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp10) | hskp11) <=> (hskp11 | hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))))),
% 0.71/0.89 inference(bind,[status(th)],[])).
% 0.71/0.89 tff(1374,plain,
% 0.71/0.89 (![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp10) | hskp11) <=> ![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))),
% 0.71/0.89 inference(quant_intro,[status(thm)],[1373])).
% 0.71/0.89 tff(1375,axiom,(![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp10) | hskp11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause135')).
% 0.71/0.89 tff(1376,plain,
% 0.71/0.89 (![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[1375, 1374])).
% 0.71/0.89 tff(1377,plain,
% 0.71/0.89 (![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[1376, 1372])).
% 0.71/0.89 tff(1378,plain,(
% 0.71/0.89 ![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))),
% 0.71/0.89 inference(skolemize,[status(sab)],[1377])).
% 0.71/0.89 tff(1379,plain,
% 0.71/0.89 (![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[1378, 1371])).
% 0.71/0.89 tff(1380,plain,
% 0.71/0.89 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp22 | c2_1(a149) | (~ndr1_0) | (~c2_1(a199)) | (~c0_1(a199)) | (~c1_1(a199)) | (~c3_1(a149)) | (~c0_1(a149)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp22 | c2_1(a149) | (~ndr1_0) | (~c2_1(a199)) | (~c0_1(a199)) | (~c1_1(a199)) | (~c3_1(a149)) | (~c0_1(a149)))),
% 0.71/0.89 inference(rewrite,[status(thm)],[])).
% 0.71/0.89 tff(1381,plain,
% 0.71/0.89 ((hskp22 | (~ndr1_0) | (~c2_1(a199)) | (~c1_1(a199)) | (~c0_1(a199)) | c2_1(a149) | (~c3_1(a149)) | (~c0_1(a149))) <=> (hskp22 | c2_1(a149) | (~ndr1_0) | (~c2_1(a199)) | (~c0_1(a199)) | (~c1_1(a199)) | (~c3_1(a149)) | (~c0_1(a149)))),
% 0.71/0.89 inference(rewrite,[status(thm)],[])).
% 0.71/0.89 tff(1382,plain,
% 0.71/0.89 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | (~c2_1(a199)) | (~c1_1(a199)) | (~c0_1(a199)) | c2_1(a149) | (~c3_1(a149)) | (~c0_1(a149)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp22 | c2_1(a149) | (~ndr1_0) | (~c2_1(a199)) | (~c0_1(a199)) | (~c1_1(a199)) | (~c3_1(a149)) | (~c0_1(a149))))),
% 0.71/0.89 inference(monotonicity,[status(thm)],[1381])).
% 0.71/0.89 tff(1383,plain,
% 0.71/0.89 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | (~c2_1(a199)) | (~c1_1(a199)) | (~c0_1(a199)) | c2_1(a149) | (~c3_1(a149)) | (~c0_1(a149)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp22 | c2_1(a149) | (~ndr1_0) | (~c2_1(a199)) | (~c0_1(a199)) | (~c1_1(a199)) | (~c3_1(a149)) | (~c0_1(a149)))),
% 0.71/0.89 inference(transitivity,[status(thm)],[1382, 1380])).
% 0.71/0.89 tff(1384,plain,
% 0.71/0.89 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | (~c2_1(a199)) | (~c1_1(a199)) | (~c0_1(a199)) | c2_1(a149) | (~c3_1(a149)) | (~c0_1(a149)))),
% 0.71/0.89 inference(quant_inst,[status(thm)],[])).
% 0.71/0.89 tff(1385,plain,
% 0.71/0.89 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp22 | c2_1(a149) | (~ndr1_0) | (~c2_1(a199)) | (~c0_1(a199)) | (~c1_1(a199)) | (~c3_1(a149)) | (~c0_1(a149))),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[1384, 1383])).
% 0.71/0.89 tff(1386,plain,
% 0.71/0.89 (hskp22 | (~c0_1(a149))),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[1385, 175, 1210, 1202, 1194, 1285, 1283, 976])).
% 0.71/0.89 tff(1387,plain,
% 0.71/0.89 (hskp22),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[1386, 1355])).
% 0.71/0.89 tff(1388,plain,
% 0.71/0.89 (~c1_1(a179)),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[989, 1387])).
% 0.71/0.89 tff(1389,plain,
% 0.71/0.89 (c2_1(a179)),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[997, 1387])).
% 0.71/0.89 tff(1390,plain,
% 0.71/0.89 (c0_1(a179)),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[1005, 1387])).
% 0.71/0.89 tff(1391,plain,
% 0.71/0.89 (hskp20 | (~c3_1(a151))),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[1012, 175, 1390, 1389, 1358, 1388, 1357, 861])).
% 0.71/0.89 tff(1392,plain,
% 0.71/0.89 (hskp20),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[1391, 1359])).
% 0.71/0.89 tff(1393,plain,
% 0.71/0.89 (~c2_1(a168)),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[873, 1392])).
% 0.71/0.89 tff(1394,plain,
% 0.71/0.89 (~c0_1(a168)),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[894, 1392])).
% 0.71/0.89 tff(1395,plain,
% 0.71/0.89 (c1_1(a168)),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[881, 1392])).
% 0.71/0.89 tff(1396,plain,
% 0.71/0.89 (((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp11 | hskp10 | c0_1(a168) | c2_1(a168) | (~ndr1_0) | (~c1_1(a168)))) <=> ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | hskp11 | hskp10 | c0_1(a168) | c2_1(a168) | (~ndr1_0) | (~c1_1(a168)))),
% 0.71/0.89 inference(rewrite,[status(thm)],[])).
% 0.71/0.89 tff(1397,plain,
% 0.71/0.89 ((hskp11 | hskp10 | (~ndr1_0) | c0_1(a168) | c2_1(a168) | (~c1_1(a168))) <=> (hskp11 | hskp10 | c0_1(a168) | c2_1(a168) | (~ndr1_0) | (~c1_1(a168)))),
% 0.71/0.89 inference(rewrite,[status(thm)],[])).
% 0.71/0.89 tff(1398,plain,
% 0.71/0.89 (((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp11 | hskp10 | (~ndr1_0) | c0_1(a168) | c2_1(a168) | (~c1_1(a168)))) <=> ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp11 | hskp10 | c0_1(a168) | c2_1(a168) | (~ndr1_0) | (~c1_1(a168))))),
% 0.71/0.89 inference(monotonicity,[status(thm)],[1397])).
% 0.71/0.89 tff(1399,plain,
% 0.71/0.89 (((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp11 | hskp10 | (~ndr1_0) | c0_1(a168) | c2_1(a168) | (~c1_1(a168)))) <=> ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | hskp11 | hskp10 | c0_1(a168) | c2_1(a168) | (~ndr1_0) | (~c1_1(a168)))),
% 0.71/0.89 inference(transitivity,[status(thm)],[1398, 1396])).
% 0.71/0.89 tff(1400,plain,
% 0.71/0.89 ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp11 | hskp10 | (~ndr1_0) | c0_1(a168) | c2_1(a168) | (~c1_1(a168)))),
% 0.71/0.89 inference(quant_inst,[status(thm)],[])).
% 0.71/0.89 tff(1401,plain,
% 0.71/0.89 ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | hskp11 | hskp10 | c0_1(a168) | c2_1(a168) | (~ndr1_0) | (~c1_1(a168))),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[1400, 1399])).
% 0.71/0.89 tff(1402,plain,
% 0.71/0.89 (hskp11),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[1401, 175, 1185, 1395, 1394, 1393, 1379])).
% 0.71/0.89 tff(1403,plain,
% 0.71/0.89 (((~hskp11) | (~c3_1(a139))) <=> ((~hskp11) | (~c3_1(a139)))),
% 0.71/0.89 inference(rewrite,[status(thm)],[])).
% 0.71/0.89 tff(1404,plain,
% 0.71/0.89 (((~c3_1(a139)) | (~hskp11)) <=> ((~hskp11) | (~c3_1(a139)))),
% 0.71/0.89 inference(rewrite,[status(thm)],[])).
% 0.71/0.89 tff(1405,axiom,((~c3_1(a139)) | (~hskp11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause112')).
% 0.71/0.89 tff(1406,plain,
% 0.71/0.89 ((~hskp11) | (~c3_1(a139))),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[1405, 1404])).
% 0.71/0.89 tff(1407,plain,
% 0.71/0.89 ((~hskp11) | (~c3_1(a139))),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[1406, 1403])).
% 0.71/0.89 tff(1408,plain,
% 0.71/0.89 (~c3_1(a139)),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[1407, 1402])).
% 0.71/0.89 tff(1409,plain,
% 0.71/0.89 (((~hskp11) | (~c1_1(a139))) <=> ((~hskp11) | (~c1_1(a139)))),
% 0.71/0.89 inference(rewrite,[status(thm)],[])).
% 0.71/0.89 tff(1410,plain,
% 0.71/0.89 (((~c1_1(a139)) | (~hskp11)) <=> ((~hskp11) | (~c1_1(a139)))),
% 0.71/0.89 inference(rewrite,[status(thm)],[])).
% 0.71/0.89 tff(1411,axiom,((~c1_1(a139)) | (~hskp11)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause111')).
% 0.71/0.89 tff(1412,plain,
% 0.71/0.89 ((~hskp11) | (~c1_1(a139))),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[1411, 1410])).
% 0.71/0.89 tff(1413,plain,
% 0.71/0.89 ((~hskp11) | (~c1_1(a139))),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[1412, 1409])).
% 0.71/0.89 tff(1414,plain,
% 0.71/0.89 (~c1_1(a139)),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[1413, 1402])).
% 0.71/0.89 tff(1415,plain,
% 0.71/0.89 (((~hskp11) | c0_1(a139)) <=> ((~hskp11) | c0_1(a139))),
% 0.71/0.89 inference(rewrite,[status(thm)],[])).
% 0.71/0.89 tff(1416,axiom,((~hskp11) | c0_1(a139)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause67')).
% 0.71/0.89 tff(1417,plain,
% 0.71/0.89 ((~hskp11) | c0_1(a139)),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[1416, 1415])).
% 0.71/0.89 tff(1418,plain,
% 0.71/0.89 ((~hskp11) | c0_1(a139)),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[1417, 1415])).
% 0.71/0.89 tff(1419,plain,
% 0.71/0.89 ((~hskp11) | c0_1(a139)),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[1418, 1415])).
% 0.71/0.89 tff(1420,plain,
% 0.71/0.89 ((~hskp11) | c0_1(a139)),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[1419, 1415])).
% 0.71/0.89 tff(1421,plain,
% 0.71/0.89 ((~hskp11) | c0_1(a139)),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[1420, 1415])).
% 0.71/0.89 tff(1422,plain,
% 0.71/0.89 (c0_1(a139)),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[1421, 1402])).
% 0.71/0.89 tff(1423,plain,
% 0.71/0.89 (c0_1(a151)),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[231, 1356])).
% 0.71/0.89 tff(1424,plain,
% 0.71/0.89 (c3_1(a168)),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[888, 175, 53, 95, 1395, 1393, 128])).
% 0.71/0.89 tff(1425,plain,
% 0.71/0.89 ((~c2_1(a145)) | (~c3_1(a168))),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[1024, 175, 52, 1394, 1393, 1303, 1302, 41])).
% 0.71/0.89 tff(1426,plain,
% 0.71/0.89 (~c2_1(a145)),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[1425, 1424])).
% 0.71/0.89 tff(1427,plain,
% 0.71/0.89 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp27 | c0_1(a168) | c2_1(a168) | c0_1(a145) | c3_1(a145) | (~ndr1_0) | c2_1(a145) | (~c3_1(a168)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp27 | c0_1(a168) | c2_1(a168) | c0_1(a145) | c3_1(a145) | (~ndr1_0) | c2_1(a145) | (~c3_1(a168)))),
% 0.71/0.89 inference(rewrite,[status(thm)],[])).
% 0.71/0.89 tff(1428,plain,
% 0.71/0.89 ((hskp27 | (~ndr1_0) | c0_1(a168) | c2_1(a168) | (~c3_1(a168)) | c3_1(a145) | c0_1(a145) | c2_1(a145)) <=> (hskp27 | c0_1(a168) | c2_1(a168) | c0_1(a145) | c3_1(a145) | (~ndr1_0) | c2_1(a145) | (~c3_1(a168)))),
% 0.71/0.89 inference(rewrite,[status(thm)],[])).
% 0.71/0.89 tff(1429,plain,
% 0.71/0.89 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp27 | (~ndr1_0) | c0_1(a168) | c2_1(a168) | (~c3_1(a168)) | c3_1(a145) | c0_1(a145) | c2_1(a145))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp27 | c0_1(a168) | c2_1(a168) | c0_1(a145) | c3_1(a145) | (~ndr1_0) | c2_1(a145) | (~c3_1(a168))))),
% 0.71/0.89 inference(monotonicity,[status(thm)],[1428])).
% 0.71/0.89 tff(1430,plain,
% 0.71/0.89 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp27 | (~ndr1_0) | c0_1(a168) | c2_1(a168) | (~c3_1(a168)) | c3_1(a145) | c0_1(a145) | c2_1(a145))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp27 | c0_1(a168) | c2_1(a168) | c0_1(a145) | c3_1(a145) | (~ndr1_0) | c2_1(a145) | (~c3_1(a168)))),
% 0.71/0.89 inference(transitivity,[status(thm)],[1429, 1427])).
% 0.71/0.89 tff(1431,plain,
% 0.71/0.89 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp27 | (~ndr1_0) | c0_1(a168) | c2_1(a168) | (~c3_1(a168)) | c3_1(a145) | c0_1(a145) | c2_1(a145))),
% 0.71/0.89 inference(quant_inst,[status(thm)],[])).
% 0.71/0.89 tff(1432,plain,
% 0.71/0.89 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp27 | c0_1(a168) | c2_1(a168) | c0_1(a145) | c3_1(a145) | (~ndr1_0) | c2_1(a145) | (~c3_1(a168))),
% 0.71/0.89 inference(modus_ponens,[status(thm)],[1431, 1430])).
% 0.71/0.89 tff(1433,plain,
% 0.71/0.89 (hskp27 | c2_1(a145) | (~c3_1(a168))),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[1432, 175, 1394, 1393, 1301, 1302, 1131])).
% 0.71/0.89 tff(1434,plain,
% 0.71/0.89 (hskp27),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[1433, 1426, 1424])).
% 0.71/0.89 tff(1435,plain,
% 0.71/0.89 (c3_1(a137)),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[1146, 1434])).
% 0.71/0.89 tff(1436,plain,
% 0.71/0.89 (c2_1(a137)),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[1154, 1434])).
% 0.71/0.89 tff(1437,plain,
% 0.71/0.89 (c1_1(a137)),
% 0.71/0.89 inference(unit_resolution,[status(thm)],[1162, 1434])).
% 0.71/0.89 tff(1438,plain,
% 0.71/0.89 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | (c2_1(a151) | c1_1(a139) | c3_1(a139) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | (~c0_1(a139)) | (~c3_1(a151)) | (~c0_1(a151)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a151) | c1_1(a139) | c3_1(a139) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | (~c0_1(a139)) | (~c3_1(a151)) | (~c0_1(a151)))),
% 0.71/0.89 inference(rewrite,[status(thm)],[])).
% 0.71/0.89 tff(1439,plain,
% 0.71/0.89 (((~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | c2_1(a151) | (~c3_1(a151)) | (~c0_1(a151)) | c1_1(a139) | c3_1(a139) | (~c0_1(a139))) <=> (c2_1(a151) | c1_1(a139) | c3_1(a139) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | (~c0_1(a139)) | (~c3_1(a151)) | (~c0_1(a151)))),
% 0.75/0.90 inference(rewrite,[status(thm)],[])).
% 0.75/0.90 tff(1440,plain,
% 0.75/0.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | c2_1(a151) | (~c3_1(a151)) | (~c0_1(a151)) | c1_1(a139) | c3_1(a139) | (~c0_1(a139)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | (c2_1(a151) | c1_1(a139) | c3_1(a139) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | (~c0_1(a139)) | (~c3_1(a151)) | (~c0_1(a151))))),
% 0.75/0.90 inference(monotonicity,[status(thm)],[1439])).
% 0.75/0.90 tff(1441,plain,
% 0.75/0.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | c2_1(a151) | (~c3_1(a151)) | (~c0_1(a151)) | c1_1(a139) | c3_1(a139) | (~c0_1(a139)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a151) | c1_1(a139) | c3_1(a139) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | (~c0_1(a139)) | (~c3_1(a151)) | (~c0_1(a151)))),
% 0.75/0.90 inference(transitivity,[status(thm)],[1440, 1438])).
% 0.75/0.90 tff(1442,plain,
% 0.75/0.90 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | c2_1(a151) | (~c3_1(a151)) | (~c0_1(a151)) | c1_1(a139) | c3_1(a139) | (~c0_1(a139)))),
% 0.75/0.90 inference(quant_inst,[status(thm)],[])).
% 0.75/0.90 tff(1443,plain,
% 0.75/0.90 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a151) | c1_1(a139) | c3_1(a139) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | (~c0_1(a139)) | (~c3_1(a151)) | (~c0_1(a151))),
% 0.75/0.90 inference(modus_ponens,[status(thm)],[1442, 1441])).
% 0.75/0.90 tff(1444,plain,
% 0.75/0.90 ($false),
% 0.75/0.90 inference(unit_resolution,[status(thm)],[1443, 175, 1437, 1436, 1435, 1423, 1422, 1357, 1414, 1408, 1369, 1359])).
% 0.75/0.90 tff(1445,plain,(hskp21 | hskp3 | hskp18), inference(lemma,lemma(discharge,[]))).
% 0.75/0.90 tff(1446,plain,
% 0.75/0.90 (hskp21),
% 0.75/0.90 inference(unit_resolution,[status(thm)],[1445, 52, 95])).
% 0.75/0.90 tff(1447,plain,
% 0.75/0.90 (~c2_1(a170)),
% 0.75/0.90 inference(unit_resolution,[status(thm)],[291, 1446])).
% 0.75/0.90 tff(1448,plain,
% 0.75/0.90 (~c0_1(a170)),
% 0.75/0.90 inference(unit_resolution,[status(thm)],[297, 1446])).
% 0.75/0.90 tff(1449,plain,
% 0.75/0.90 (c3_1(a170)),
% 0.75/0.90 inference(unit_resolution,[status(thm)],[322, 1446])).
% 0.75/0.90 tff(1450,plain,
% 0.75/0.90 (hskp14),
% 0.75/0.90 inference(unit_resolution,[status(thm)],[482, 175, 52, 1449, 1448, 1447, 51])).
% 0.75/0.90 tff(1451,plain,
% 0.75/0.90 (~c0_1(a145)),
% 0.75/0.90 inference(unit_resolution,[status(thm)],[508, 1450])).
% 0.75/0.90 tff(1452,plain,
% 0.75/0.90 (~c3_1(a145)),
% 0.75/0.90 inference(unit_resolution,[status(thm)],[489, 1450])).
% 0.75/0.90 tff(1453,plain,
% 0.75/0.90 (~c1_1(a145)),
% 0.75/0.90 inference(unit_resolution,[status(thm)],[495, 1450])).
% 0.75/0.90 tff(1454,plain,
% 0.75/0.90 (c0_1(a149)),
% 0.75/0.90 inference(unit_resolution,[status(thm)],[1354, 1453, 1452, 52, 1285, 1283, 1451])).
% 0.75/0.90 tff(1455,plain,
% 0.75/0.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a170) | c2_1(a170) | c1_1(a149) | c2_1(a149) | c0_1(a145) | c1_1(a145) | c3_1(a145) | (~ndr1_0) | (~c0_1(a149)) | c1_1(a170))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a170) | c2_1(a170) | c1_1(a149) | c2_1(a149) | c0_1(a145) | c1_1(a145) | c3_1(a145) | (~ndr1_0) | (~c0_1(a149)) | c1_1(a170))),
% 0.75/0.90 inference(rewrite,[status(thm)],[])).
% 0.75/0.90 tff(1456,plain,
% 0.75/0.90 (((~ndr1_0) | c1_1(a149) | c2_1(a149) | (~c0_1(a149)) | c3_1(a145) | c1_1(a145) | c0_1(a145) | c2_1(a170) | c1_1(a170) | c0_1(a170)) <=> (c0_1(a170) | c2_1(a170) | c1_1(a149) | c2_1(a149) | c0_1(a145) | c1_1(a145) | c3_1(a145) | (~ndr1_0) | (~c0_1(a149)) | c1_1(a170))),
% 0.75/0.90 inference(rewrite,[status(thm)],[])).
% 0.75/0.90 tff(1457,plain,
% 0.75/0.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a149) | c2_1(a149) | (~c0_1(a149)) | c3_1(a145) | c1_1(a145) | c0_1(a145) | c2_1(a170) | c1_1(a170) | c0_1(a170))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a170) | c2_1(a170) | c1_1(a149) | c2_1(a149) | c0_1(a145) | c1_1(a145) | c3_1(a145) | (~ndr1_0) | (~c0_1(a149)) | c1_1(a170)))),
% 0.75/0.90 inference(monotonicity,[status(thm)],[1456])).
% 0.75/0.90 tff(1458,plain,
% 0.75/0.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a149) | c2_1(a149) | (~c0_1(a149)) | c3_1(a145) | c1_1(a145) | c0_1(a145) | c2_1(a170) | c1_1(a170) | c0_1(a170))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a170) | c2_1(a170) | c1_1(a149) | c2_1(a149) | c0_1(a145) | c1_1(a145) | c3_1(a145) | (~ndr1_0) | (~c0_1(a149)) | c1_1(a170))),
% 0.75/0.90 inference(transitivity,[status(thm)],[1457, 1455])).
% 0.75/0.90 tff(1459,plain,
% 0.75/0.90 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a149) | c2_1(a149) | (~c0_1(a149)) | c3_1(a145) | c1_1(a145) | c0_1(a145) | c2_1(a170) | c1_1(a170) | c0_1(a170))),
% 0.75/0.90 inference(quant_inst,[status(thm)],[])).
% 0.75/0.90 tff(1460,plain,
% 0.75/0.90 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a170) | c2_1(a170) | c1_1(a149) | c2_1(a149) | c0_1(a145) | c1_1(a145) | c3_1(a145) | (~ndr1_0) | (~c0_1(a149)) | c1_1(a170)),
% 0.75/0.90 inference(modus_ponens,[status(thm)],[1459, 1458])).
% 0.75/0.90 tff(1461,plain,
% 0.75/0.90 (c1_1(a170)),
% 0.75/0.90 inference(unit_resolution,[status(thm)],[1460, 175, 1448, 1447, 1284, 1283, 1451, 1453, 1452, 460, 1454])).
% 0.75/0.90 tff(1462,plain,
% 0.75/0.90 (((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp11 | hskp10 | c0_1(a170) | c2_1(a170) | (~ndr1_0) | (~c1_1(a170)))) <=> ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | hskp11 | hskp10 | c0_1(a170) | c2_1(a170) | (~ndr1_0) | (~c1_1(a170)))),
% 0.75/0.90 inference(rewrite,[status(thm)],[])).
% 0.75/0.90 tff(1463,plain,
% 0.75/0.90 ((hskp11 | hskp10 | (~ndr1_0) | c0_1(a170) | c2_1(a170) | (~c1_1(a170))) <=> (hskp11 | hskp10 | c0_1(a170) | c2_1(a170) | (~ndr1_0) | (~c1_1(a170)))),
% 0.75/0.90 inference(rewrite,[status(thm)],[])).
% 0.75/0.90 tff(1464,plain,
% 0.75/0.90 (((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp11 | hskp10 | (~ndr1_0) | c0_1(a170) | c2_1(a170) | (~c1_1(a170)))) <=> ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp11 | hskp10 | c0_1(a170) | c2_1(a170) | (~ndr1_0) | (~c1_1(a170))))),
% 0.75/0.90 inference(monotonicity,[status(thm)],[1463])).
% 0.75/0.90 tff(1465,plain,
% 0.75/0.90 (((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp11 | hskp10 | (~ndr1_0) | c0_1(a170) | c2_1(a170) | (~c1_1(a170)))) <=> ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | hskp11 | hskp10 | c0_1(a170) | c2_1(a170) | (~ndr1_0) | (~c1_1(a170)))),
% 0.75/0.90 inference(transitivity,[status(thm)],[1464, 1462])).
% 0.75/0.90 tff(1466,plain,
% 0.75/0.90 ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp11 | hskp10 | (~ndr1_0) | c0_1(a170) | c2_1(a170) | (~c1_1(a170)))),
% 0.75/0.90 inference(quant_inst,[status(thm)],[])).
% 0.75/0.90 tff(1467,plain,
% 0.75/0.90 ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | hskp11 | hskp10 | c0_1(a170) | c2_1(a170) | (~ndr1_0) | (~c1_1(a170))),
% 0.75/0.90 inference(modus_ponens,[status(thm)],[1466, 1465])).
% 0.75/0.90 tff(1468,plain,
% 0.75/0.90 (hskp11 | (~c1_1(a170))),
% 0.75/0.90 inference(unit_resolution,[status(thm)],[1467, 175, 1185, 1448, 1447, 1379])).
% 0.75/0.90 tff(1469,plain,
% 0.75/0.90 (hskp11),
% 0.75/0.90 inference(unit_resolution,[status(thm)],[1468, 1461])).
% 0.75/0.90 tff(1470,plain,
% 0.75/0.90 (~c3_1(a139)),
% 0.75/0.90 inference(unit_resolution,[status(thm)],[1407, 1469])).
% 0.75/0.90 tff(1471,plain,
% 0.75/0.90 (~c1_1(a139)),
% 0.75/0.90 inference(unit_resolution,[status(thm)],[1413, 1469])).
% 0.75/0.90 tff(1472,plain,
% 0.75/0.90 (c0_1(a139)),
% 0.75/0.90 inference(unit_resolution,[status(thm)],[1421, 1469])).
% 0.75/0.90 tff(1473,plain,
% 0.75/0.90 (~c2_1(a145)),
% 0.75/0.90 inference(unit_resolution,[status(thm)],[502, 175, 52, 1449, 1448, 1447, 1453, 1452, 41])).
% 0.75/0.90 tff(1474,plain,
% 0.75/0.90 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp27 | c0_1(a170) | c2_1(a170) | c0_1(a145) | c3_1(a145) | (~ndr1_0) | c2_1(a145) | (~c3_1(a170)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp27 | c0_1(a170) | c2_1(a170) | c0_1(a145) | c3_1(a145) | (~ndr1_0) | c2_1(a145) | (~c3_1(a170)))),
% 0.75/0.90 inference(rewrite,[status(thm)],[])).
% 0.75/0.90 tff(1475,plain,
% 0.75/0.90 ((hskp27 | (~ndr1_0) | c0_1(a170) | c2_1(a170) | (~c3_1(a170)) | c3_1(a145) | c0_1(a145) | c2_1(a145)) <=> (hskp27 | c0_1(a170) | c2_1(a170) | c0_1(a145) | c3_1(a145) | (~ndr1_0) | c2_1(a145) | (~c3_1(a170)))),
% 0.75/0.90 inference(rewrite,[status(thm)],[])).
% 0.75/0.90 tff(1476,plain,
% 0.75/0.90 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp27 | (~ndr1_0) | c0_1(a170) | c2_1(a170) | (~c3_1(a170)) | c3_1(a145) | c0_1(a145) | c2_1(a145))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp27 | c0_1(a170) | c2_1(a170) | c0_1(a145) | c3_1(a145) | (~ndr1_0) | c2_1(a145) | (~c3_1(a170))))),
% 0.75/0.90 inference(monotonicity,[status(thm)],[1475])).
% 0.75/0.90 tff(1477,plain,
% 0.75/0.90 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp27 | (~ndr1_0) | c0_1(a170) | c2_1(a170) | (~c3_1(a170)) | c3_1(a145) | c0_1(a145) | c2_1(a145))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp27 | c0_1(a170) | c2_1(a170) | c0_1(a145) | c3_1(a145) | (~ndr1_0) | c2_1(a145) | (~c3_1(a170)))),
% 0.75/0.90 inference(transitivity,[status(thm)],[1476, 1474])).
% 0.75/0.90 tff(1478,plain,
% 0.75/0.90 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp27 | (~ndr1_0) | c0_1(a170) | c2_1(a170) | (~c3_1(a170)) | c3_1(a145) | c0_1(a145) | c2_1(a145))),
% 0.75/0.90 inference(quant_inst,[status(thm)],[])).
% 0.75/0.90 tff(1479,plain,
% 0.75/0.90 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp27 | c0_1(a170) | c2_1(a170) | c0_1(a145) | c3_1(a145) | (~ndr1_0) | c2_1(a145) | (~c3_1(a170))),
% 0.75/0.90 inference(modus_ponens,[status(thm)],[1478, 1477])).
% 0.75/0.90 tff(1480,plain,
% 0.75/0.90 (hskp27),
% 0.75/0.90 inference(unit_resolution,[status(thm)],[1479, 175, 1449, 1448, 1447, 1451, 1452, 1131, 1473])).
% 0.75/0.90 tff(1481,plain,
% 0.75/0.90 (c3_1(a137)),
% 0.75/0.90 inference(unit_resolution,[status(thm)],[1146, 1480])).
% 0.75/0.90 tff(1482,plain,
% 0.75/0.90 (c2_1(a137)),
% 0.75/0.90 inference(unit_resolution,[status(thm)],[1154, 1480])).
% 0.75/0.90 tff(1483,plain,
% 0.75/0.90 (c1_1(a137)),
% 0.75/0.90 inference(unit_resolution,[status(thm)],[1162, 1480])).
% 0.75/0.90 tff(1484,plain,
% 0.75/0.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | (c2_1(a149) | c1_1(a139) | c3_1(a139) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | (~c0_1(a139)) | (~c3_1(a149)) | (~c0_1(a149)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a149) | c1_1(a139) | c3_1(a139) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | (~c0_1(a139)) | (~c3_1(a149)) | (~c0_1(a149)))),
% 0.75/0.90 inference(rewrite,[status(thm)],[])).
% 0.75/0.90 tff(1485,plain,
% 0.75/0.90 (((~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | c2_1(a149) | (~c3_1(a149)) | (~c0_1(a149)) | c1_1(a139) | c3_1(a139) | (~c0_1(a139))) <=> (c2_1(a149) | c1_1(a139) | c3_1(a139) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | (~c0_1(a139)) | (~c3_1(a149)) | (~c0_1(a149)))),
% 0.75/0.90 inference(rewrite,[status(thm)],[])).
% 0.75/0.90 tff(1486,plain,
% 0.75/0.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | c2_1(a149) | (~c3_1(a149)) | (~c0_1(a149)) | c1_1(a139) | c3_1(a139) | (~c0_1(a139)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | (c2_1(a149) | c1_1(a139) | c3_1(a139) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | (~c0_1(a139)) | (~c3_1(a149)) | (~c0_1(a149))))),
% 0.75/0.90 inference(monotonicity,[status(thm)],[1485])).
% 0.75/0.90 tff(1487,plain,
% 0.75/0.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | c2_1(a149) | (~c3_1(a149)) | (~c0_1(a149)) | c1_1(a139) | c3_1(a139) | (~c0_1(a139)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a149) | c1_1(a139) | c3_1(a139) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | (~c0_1(a139)) | (~c3_1(a149)) | (~c0_1(a149)))),
% 0.75/0.90 inference(transitivity,[status(thm)],[1486, 1484])).
% 0.75/0.90 tff(1488,plain,
% 0.75/0.90 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | ((~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | c2_1(a149) | (~c3_1(a149)) | (~c0_1(a149)) | c1_1(a139) | c3_1(a139) | (~c0_1(a139)))),
% 0.75/0.90 inference(quant_inst,[status(thm)],[])).
% 0.75/0.90 tff(1489,plain,
% 0.75/0.90 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c0_1(W)))) | c2_1(a149) | c1_1(a139) | c3_1(a139) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | (~c0_1(a139)) | (~c3_1(a149)) | (~c0_1(a149))),
% 0.75/0.90 inference(modus_ponens,[status(thm)],[1488, 1487])).
% 0.75/0.90 tff(1490,plain,
% 0.75/0.90 ($false),
% 0.75/0.90 inference(unit_resolution,[status(thm)],[1489, 175, 1483, 1482, 1481, 1285, 1472, 1283, 1471, 1470, 1369, 1454])).
% 0.75/0.90 tff(1491,plain,(hskp3 | hskp18), inference(lemma,lemma(discharge,[]))).
% 0.75/0.90 tff(1492,plain,
% 0.75/0.90 (hskp3),
% 0.75/0.90 inference(unit_resolution,[status(thm)],[1491, 95])).
% 0.75/0.90 tff(1493,plain,
% 0.75/0.90 (~c0_1(a128)),
% 0.75/0.90 inference(unit_resolution,[status(thm)],[475, 1492])).
% 0.75/0.90 tff(1494,plain,
% 0.75/0.90 (~c2_1(a128)),
% 0.75/0.90 inference(unit_resolution,[status(thm)],[550, 1492])).
% 0.75/0.90 tff(1495,plain,
% 0.75/0.90 (~c3_1(a128)),
% 0.75/0.90 inference(unit_resolution,[status(thm)],[1043, 1492])).
% 0.75/0.90 tff(1496,assumption,(~c3_1(a199)), introduced(assumption)).
% 0.75/0.90 tff(1497,plain,
% 0.75/0.90 (hskp13),
% 0.75/0.90 inference(unit_resolution,[status(thm)],[1238, 175, 1222, 1221, 1232, 21, 1496])).
% 0.75/0.90 tff(1498,plain,
% 0.75/0.90 (~c3_1(a144)),
% 0.75/0.90 inference(unit_resolution,[status(thm)],[928, 1497])).
% 0.75/0.90 tff(1499,plain,
% 0.75/0.90 (~c0_1(a144)),
% 0.75/0.90 inference(unit_resolution,[status(thm)],[949, 1497])).
% 0.75/0.90 tff(1500,plain,
% 0.75/0.90 (c2_1(a144)),
% 0.75/0.90 inference(unit_resolution,[status(thm)],[936, 1497])).
% 0.75/0.90 tff(1501,assumption,(~c3_1(a144)), introduced(assumption)).
% 0.75/0.90 tff(1502,assumption,(~c0_1(a144)), introduced(assumption)).
% 0.75/0.90 tff(1503,assumption,(c2_1(a144)), introduced(assumption)).
% 0.75/0.90 tff(1504,assumption,(hskp27), introduced(assumption)).
% 0.75/0.90 tff(1505,plain,
% 0.75/0.90 (c3_1(a137)),
% 0.75/0.90 inference(unit_resolution,[status(thm)],[1146, 1504])).
% 0.75/0.90 tff(1506,plain,
% 0.75/0.90 (c2_1(a137)),
% 0.75/0.90 inference(unit_resolution,[status(thm)],[1154, 1504])).
% 0.75/0.90 tff(1507,plain,
% 0.75/0.90 (c1_1(a137)),
% 0.75/0.90 inference(unit_resolution,[status(thm)],[1162, 1504])).
% 0.75/0.90 tff(1508,plain,
% 0.75/0.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c0_1(a144) | c3_1(a144) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | c1_1(a128) | (~c2_1(a144)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c0_1(a144) | c3_1(a144) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | c1_1(a128) | (~c2_1(a144)))),
% 0.75/0.90 inference(rewrite,[status(thm)],[])).
% 0.75/0.90 tff(1509,plain,
% 0.75/0.90 (((~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | c3_1(a144) | c0_1(a144) | (~c2_1(a144)) | c2_1(a128) | c1_1(a128) | c3_1(a128)) <=> (c0_1(a144) | c3_1(a144) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | c1_1(a128) | (~c2_1(a144)))),
% 0.75/0.90 inference(rewrite,[status(thm)],[])).
% 0.75/0.90 tff(1510,plain,
% 0.75/0.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | c3_1(a144) | c0_1(a144) | (~c2_1(a144)) | c2_1(a128) | c1_1(a128) | c3_1(a128))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c0_1(a144) | c3_1(a144) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | c1_1(a128) | (~c2_1(a144))))),
% 0.75/0.90 inference(monotonicity,[status(thm)],[1509])).
% 0.75/0.90 tff(1511,plain,
% 0.75/0.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | c3_1(a144) | c0_1(a144) | (~c2_1(a144)) | c2_1(a128) | c1_1(a128) | c3_1(a128))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c0_1(a144) | c3_1(a144) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | c1_1(a128) | (~c2_1(a144)))),
% 0.75/0.90 inference(transitivity,[status(thm)],[1510, 1508])).
% 0.75/0.90 tff(1512,plain,
% 0.75/0.90 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | c3_1(a144) | c0_1(a144) | (~c2_1(a144)) | c2_1(a128) | c1_1(a128) | c3_1(a128))),
% 0.75/0.90 inference(quant_inst,[status(thm)],[])).
% 0.75/0.90 tff(1513,plain,
% 0.75/0.90 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c0_1(a144) | c3_1(a144) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | c1_1(a128) | (~c2_1(a144))),
% 0.75/0.90 inference(modus_ponens,[status(thm)],[1512, 1511])).
% 0.75/0.90 tff(1514,plain,
% 0.75/0.90 ($false),
% 0.75/0.90 inference(unit_resolution,[status(thm)],[1513, 175, 1507, 1506, 1505, 1503, 1502, 1501, 259, 248, 1104, 534])).
% 0.75/0.90 tff(1515,plain,((~hskp27) | (~c2_1(a144)) | c0_1(a144) | c3_1(a144) | c2_1(a128) | c3_1(a128) | c1_1(a128)), inference(lemma,lemma(discharge,[]))).
% 0.75/0.90 tff(1516,plain,
% 0.75/0.90 (~hskp27),
% 0.75/0.90 inference(unit_resolution,[status(thm)],[1515, 1500, 1499, 1498, 259, 248, 534])).
% 0.75/0.90 tff(1517,plain,
% 0.75/0.90 (((~![U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp12 | (~ndr1_0) | (~c0_1(a199)) | c3_1(a199) | (~c1_1(a199)))) <=> ((~![U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp12 | (~ndr1_0) | (~c0_1(a199)) | c3_1(a199) | (~c1_1(a199)))),
% 0.75/0.90 inference(rewrite,[status(thm)],[])).
% 0.75/0.90 tff(1518,plain,
% 0.75/0.90 ((hskp12 | (~ndr1_0) | c3_1(a199) | (~c1_1(a199)) | (~c0_1(a199))) <=> (hskp12 | (~ndr1_0) | (~c0_1(a199)) | c3_1(a199) | (~c1_1(a199)))),
% 0.75/0.90 inference(rewrite,[status(thm)],[])).
% 0.75/0.90 tff(1519,plain,
% 0.75/0.90 (((~![U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp12 | (~ndr1_0) | c3_1(a199) | (~c1_1(a199)) | (~c0_1(a199)))) <=> ((~![U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp12 | (~ndr1_0) | (~c0_1(a199)) | c3_1(a199) | (~c1_1(a199))))),
% 0.75/0.90 inference(monotonicity,[status(thm)],[1518])).
% 0.75/0.90 tff(1520,plain,
% 0.75/0.90 (((~![U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp12 | (~ndr1_0) | c3_1(a199) | (~c1_1(a199)) | (~c0_1(a199)))) <=> ((~![U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp12 | (~ndr1_0) | (~c0_1(a199)) | c3_1(a199) | (~c1_1(a199)))),
% 0.75/0.90 inference(transitivity,[status(thm)],[1519, 1517])).
% 0.75/0.90 tff(1521,plain,
% 0.75/0.90 ((~![U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp12 | (~ndr1_0) | c3_1(a199) | (~c1_1(a199)) | (~c0_1(a199)))),
% 0.75/0.90 inference(quant_inst,[status(thm)],[])).
% 0.75/0.90 tff(1522,plain,
% 0.75/0.90 ((~![U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp12 | (~ndr1_0) | (~c0_1(a199)) | c3_1(a199) | (~c1_1(a199))),
% 0.75/0.90 inference(modus_ponens,[status(thm)],[1521, 1520])).
% 0.75/0.90 tff(1523,plain,
% 0.75/0.90 (hskp12 | c3_1(a199)),
% 0.75/0.90 inference(unit_resolution,[status(thm)],[1522, 175, 1222, 1221, 224])).
% 0.75/0.90 tff(1524,plain,
% 0.75/0.90 (hskp12),
% 0.75/0.90 inference(unit_resolution,[status(thm)],[1523, 1496])).
% 0.75/0.90 tff(1525,plain,
% 0.75/0.90 (~c0_1(a140)),
% 0.75/0.90 inference(unit_resolution,[status(thm)],[593, 1524])).
% 0.75/0.90 tff(1526,plain,
% 0.75/0.90 (c3_1(a140)),
% 0.75/0.90 inference(unit_resolution,[status(thm)],[604, 1524])).
% 0.75/0.90 tff(1527,plain,
% 0.75/0.90 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp27 | c0_1(a140) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | c2_1(a140) | (~c3_1(a140)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp27 | c0_1(a140) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | c2_1(a140) | (~c3_1(a140)))),
% 0.75/0.90 inference(rewrite,[status(thm)],[])).
% 0.75/0.90 tff(1528,plain,
% 0.75/0.90 ((hskp27 | (~ndr1_0) | c0_1(a140) | c2_1(a140) | (~c3_1(a140)) | c3_1(a128) | c0_1(a128) | c2_1(a128)) <=> (hskp27 | c0_1(a140) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | c2_1(a140) | (~c3_1(a140)))),
% 0.75/0.90 inference(rewrite,[status(thm)],[])).
% 0.75/0.90 tff(1529,plain,
% 0.75/0.90 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp27 | (~ndr1_0) | c0_1(a140) | c2_1(a140) | (~c3_1(a140)) | c3_1(a128) | c0_1(a128) | c2_1(a128))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp27 | c0_1(a140) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | c2_1(a140) | (~c3_1(a140))))),
% 0.75/0.90 inference(monotonicity,[status(thm)],[1528])).
% 0.75/0.90 tff(1530,plain,
% 0.75/0.90 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp27 | (~ndr1_0) | c0_1(a140) | c2_1(a140) | (~c3_1(a140)) | c3_1(a128) | c0_1(a128) | c2_1(a128))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp27 | c0_1(a140) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | c2_1(a140) | (~c3_1(a140)))),
% 0.75/0.90 inference(transitivity,[status(thm)],[1529, 1527])).
% 0.75/0.90 tff(1531,plain,
% 0.75/0.90 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp27 | (~ndr1_0) | c0_1(a140) | c2_1(a140) | (~c3_1(a140)) | c3_1(a128) | c0_1(a128) | c2_1(a128))),
% 0.75/0.90 inference(quant_inst,[status(thm)],[])).
% 0.75/0.90 tff(1532,plain,
% 0.75/0.90 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp27 | c0_1(a140) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | c2_1(a140) | (~c3_1(a140))),
% 0.75/0.90 inference(modus_ponens,[status(thm)],[1531, 1530])).
% 0.75/0.90 tff(1533,plain,
% 0.75/0.90 (hskp27 | c2_1(a140)),
% 0.75/0.90 inference(unit_resolution,[status(thm)],[1532, 175, 1526, 1525, 270, 259, 248, 1131])).
% 0.75/0.90 tff(1534,plain,
% 0.75/0.90 (c2_1(a140)),
% 0.75/0.90 inference(unit_resolution,[status(thm)],[1533, 1516])).
% 0.75/0.90 tff(1535,plain,
% 0.75/0.90 (c1_1(a140)),
% 0.75/0.90 inference(unit_resolution,[status(thm)],[801, 1524])).
% 0.75/0.90 tff(1536,plain,
% 0.75/0.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c0_1(a144) | c3_1(a144) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | c1_1(a128) | (~c2_1(a140)) | (~c3_1(a140)) | (~c1_1(a140)) | (~c2_1(a144)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c0_1(a144) | c3_1(a144) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | c1_1(a128) | (~c2_1(a140)) | (~c3_1(a140)) | (~c1_1(a140)) | (~c2_1(a144)))),
% 0.75/0.90 inference(rewrite,[status(thm)],[])).
% 0.75/0.90 tff(1537,plain,
% 0.75/0.90 (((~ndr1_0) | (~c2_1(a140)) | (~c3_1(a140)) | (~c1_1(a140)) | c3_1(a144) | c0_1(a144) | (~c2_1(a144)) | c2_1(a128) | c1_1(a128) | c3_1(a128)) <=> (c0_1(a144) | c3_1(a144) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | c1_1(a128) | (~c2_1(a140)) | (~c3_1(a140)) | (~c1_1(a140)) | (~c2_1(a144)))),
% 0.75/0.90 inference(rewrite,[status(thm)],[])).
% 0.75/0.90 tff(1538,plain,
% 0.75/0.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | (~c2_1(a140)) | (~c3_1(a140)) | (~c1_1(a140)) | c3_1(a144) | c0_1(a144) | (~c2_1(a144)) | c2_1(a128) | c1_1(a128) | c3_1(a128))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c0_1(a144) | c3_1(a144) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | c1_1(a128) | (~c2_1(a140)) | (~c3_1(a140)) | (~c1_1(a140)) | (~c2_1(a144))))),
% 0.75/0.90 inference(monotonicity,[status(thm)],[1537])).
% 0.75/0.90 tff(1539,plain,
% 0.75/0.90 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | (~c2_1(a140)) | (~c3_1(a140)) | (~c1_1(a140)) | c3_1(a144) | c0_1(a144) | (~c2_1(a144)) | c2_1(a128) | c1_1(a128) | c3_1(a128))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c0_1(a144) | c3_1(a144) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | c1_1(a128) | (~c2_1(a140)) | (~c3_1(a140)) | (~c1_1(a140)) | (~c2_1(a144)))),
% 0.75/0.90 inference(transitivity,[status(thm)],[1538, 1536])).
% 0.75/0.90 tff(1540,plain,
% 0.75/0.90 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | (~c2_1(a140)) | (~c3_1(a140)) | (~c1_1(a140)) | c3_1(a144) | c0_1(a144) | (~c2_1(a144)) | c2_1(a128) | c1_1(a128) | c3_1(a128))),
% 0.75/0.90 inference(quant_inst,[status(thm)],[])).
% 0.75/0.90 tff(1541,plain,
% 0.75/0.90 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c0_1(a144) | c3_1(a144) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | c1_1(a128) | (~c2_1(a140)) | (~c3_1(a140)) | (~c1_1(a140)) | (~c2_1(a144))),
% 0.75/0.90 inference(modus_ponens,[status(thm)],[1540, 1539])).
% 0.75/0.90 tff(1542,plain,
% 0.75/0.90 ($false),
% 0.75/0.90 inference(unit_resolution,[status(thm)],[1541, 175, 1500, 1535, 1526, 1499, 1498, 259, 248, 1104, 534, 1534])).
% 0.75/0.90 tff(1543,plain,(c3_1(a199) | c2_1(a128) | c3_1(a128) | c1_1(a128) | c0_1(a128) | (~c0_1(a199)) | (~c1_1(a199)) | (~c2_1(a199))), inference(lemma,lemma(discharge,[]))).
% 0.75/0.90 tff(1544,plain,
% 0.75/0.90 (c3_1(a199)),
% 0.75/0.90 inference(unit_resolution,[status(thm)],[1543, 534, 1495, 1494, 1493, 1210, 1202, 1194])).
% 0.75/0.90 tff(1545,plain,
% 0.75/0.90 (^[U: $i] : refl((hskp18 | hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) <=> (hskp18 | hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))))),
% 0.75/0.90 inference(bind,[status(th)],[])).
% 0.75/0.90 tff(1546,plain,
% 0.75/0.90 (![U: $i] : (hskp18 | hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp18 | hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))),
% 0.75/0.90 inference(quant_intro,[status(thm)],[1545])).
% 0.75/0.90 tff(1547,plain,
% 0.75/0.90 (![U: $i] : (hskp18 | hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp18 | hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))),
% 0.75/0.90 inference(rewrite,[status(thm)],[])).
% 0.75/0.90 tff(1548,plain,
% 0.75/0.90 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp18) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | hskp18))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | hskp18) <=> (hskp18 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))), ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp18) <=> (hskp18 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp18) | hskp12) <=> ((hskp18 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | hskp12))), rewrite(((hskp18 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U))) | hskp12) <=> (hskp18 | hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))), (((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp18) | hskp12) <=> (hskp18 | hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))))),
% 0.75/0.91 inference(bind,[status(th)],[])).
% 0.75/0.91 tff(1549,plain,
% 0.75/0.91 (![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp18) | hskp12) <=> ![U: $i] : (hskp18 | hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))),
% 0.75/0.91 inference(quant_intro,[status(thm)],[1548])).
% 0.75/0.91 tff(1550,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | hskp18) | hskp12)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause158')).
% 0.75/0.91 tff(1551,plain,
% 0.75/0.91 (![U: $i] : (hskp18 | hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))),
% 0.75/0.91 inference(modus_ponens,[status(thm)],[1550, 1549])).
% 0.75/0.91 tff(1552,plain,
% 0.75/0.91 (![U: $i] : (hskp18 | hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))),
% 0.75/0.91 inference(modus_ponens,[status(thm)],[1551, 1547])).
% 0.75/0.91 tff(1553,plain,(
% 0.75/0.91 ![U: $i] : (hskp18 | hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))),
% 0.75/0.91 inference(skolemize,[status(sab)],[1552])).
% 0.75/0.91 tff(1554,plain,
% 0.75/0.91 (![U: $i] : (hskp18 | hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))),
% 0.75/0.91 inference(modus_ponens,[status(thm)],[1553, 1546])).
% 0.75/0.91 tff(1555,plain,
% 0.75/0.91 (((~![U: $i] : (hskp18 | hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp18 | hskp12 | (~ndr1_0) | (~c2_1(a199)) | (~c3_1(a199)) | (~c1_1(a199)))) <=> ((~![U: $i] : (hskp18 | hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | hskp18 | hskp12 | (~ndr1_0) | (~c2_1(a199)) | (~c3_1(a199)) | (~c1_1(a199)))),
% 0.75/0.91 inference(rewrite,[status(thm)],[])).
% 0.75/0.91 tff(1556,plain,
% 0.75/0.91 ((~![U: $i] : (hskp18 | hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | (hskp18 | hskp12 | (~ndr1_0) | (~c2_1(a199)) | (~c3_1(a199)) | (~c1_1(a199)))),
% 0.75/0.91 inference(quant_inst,[status(thm)],[])).
% 0.75/0.91 tff(1557,plain,
% 0.75/0.91 ((~![U: $i] : (hskp18 | hskp12 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)))) | hskp18 | hskp12 | (~ndr1_0) | (~c2_1(a199)) | (~c3_1(a199)) | (~c1_1(a199))),
% 0.75/0.91 inference(modus_ponens,[status(thm)],[1556, 1555])).
% 0.75/0.91 tff(1558,plain,
% 0.75/0.91 (hskp12 | (~c3_1(a199))),
% 0.75/0.91 inference(unit_resolution,[status(thm)],[1557, 175, 95, 1202, 1194, 1554])).
% 0.75/0.91 tff(1559,plain,
% 0.75/0.91 (hskp12),
% 0.75/0.91 inference(unit_resolution,[status(thm)],[1558, 1544])).
% 0.75/0.91 tff(1560,plain,
% 0.75/0.91 (~c0_1(a140)),
% 0.75/0.91 inference(unit_resolution,[status(thm)],[593, 1559])).
% 0.75/0.91 tff(1561,plain,
% 0.75/0.91 (c1_1(a140)),
% 0.75/0.91 inference(unit_resolution,[status(thm)],[801, 1559])).
% 0.75/0.91 tff(1562,plain,
% 0.75/0.91 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp18 | c0_1(a140) | (~ndr1_0) | (~c2_1(a199)) | (~c0_1(a199)) | (~c3_1(a199)) | (~c2_1(a140)) | (~c1_1(a140)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp18 | c0_1(a140) | (~ndr1_0) | (~c2_1(a199)) | (~c0_1(a199)) | (~c3_1(a199)) | (~c2_1(a140)) | (~c1_1(a140)))),
% 0.75/0.91 inference(rewrite,[status(thm)],[])).
% 0.75/0.91 tff(1563,plain,
% 0.75/0.91 ((hskp18 | (~ndr1_0) | (~c2_1(a199)) | (~c3_1(a199)) | (~c0_1(a199)) | c0_1(a140) | (~c2_1(a140)) | (~c1_1(a140))) <=> (hskp18 | c0_1(a140) | (~ndr1_0) | (~c2_1(a199)) | (~c0_1(a199)) | (~c3_1(a199)) | (~c2_1(a140)) | (~c1_1(a140)))),
% 0.75/0.91 inference(rewrite,[status(thm)],[])).
% 0.75/0.91 tff(1564,plain,
% 0.75/0.91 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp18 | (~ndr1_0) | (~c2_1(a199)) | (~c3_1(a199)) | (~c0_1(a199)) | c0_1(a140) | (~c2_1(a140)) | (~c1_1(a140)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp18 | c0_1(a140) | (~ndr1_0) | (~c2_1(a199)) | (~c0_1(a199)) | (~c3_1(a199)) | (~c2_1(a140)) | (~c1_1(a140))))),
% 0.75/0.91 inference(monotonicity,[status(thm)],[1563])).
% 0.75/0.91 tff(1565,plain,
% 0.75/0.91 (((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp18 | (~ndr1_0) | (~c2_1(a199)) | (~c3_1(a199)) | (~c0_1(a199)) | c0_1(a140) | (~c2_1(a140)) | (~c1_1(a140)))) <=> ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp18 | c0_1(a140) | (~ndr1_0) | (~c2_1(a199)) | (~c0_1(a199)) | (~c3_1(a199)) | (~c2_1(a140)) | (~c1_1(a140)))),
% 0.75/0.91 inference(transitivity,[status(thm)],[1564, 1562])).
% 0.75/0.91 tff(1566,plain,
% 0.75/0.91 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | (hskp18 | (~ndr1_0) | (~c2_1(a199)) | (~c3_1(a199)) | (~c0_1(a199)) | c0_1(a140) | (~c2_1(a140)) | (~c1_1(a140)))),
% 0.75/0.91 inference(quant_inst,[status(thm)],[])).
% 0.75/0.91 tff(1567,plain,
% 0.75/0.91 ((~![V: $i, U: $i] : (hskp18 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c0_1(V) | (~c2_1(V)) | (~c1_1(V)))) | hskp18 | c0_1(a140) | (~ndr1_0) | (~c2_1(a199)) | (~c0_1(a199)) | (~c3_1(a199)) | (~c2_1(a140)) | (~c1_1(a140))),
% 0.75/0.91 inference(modus_ponens,[status(thm)],[1566, 1565])).
% 0.75/0.91 tff(1568,plain,
% 0.75/0.91 (~c2_1(a140)),
% 0.75/0.91 inference(unit_resolution,[status(thm)],[1567, 175, 95, 1210, 1194, 1561, 1560, 635, 1544])).
% 0.75/0.91 tff(1569,plain,
% 0.75/0.91 (hskp15 | (~c3_1(a199))),
% 0.75/0.91 inference(unit_resolution,[status(thm)],[1229, 175, 1185, 1210, 1202, 1220])).
% 0.75/0.91 tff(1570,plain,
% 0.75/0.91 (hskp15),
% 0.75/0.91 inference(unit_resolution,[status(thm)],[1569, 1544])).
% 0.75/0.91 tff(1571,plain,
% 0.75/0.91 (~c1_1(a149)),
% 0.75/0.91 inference(unit_resolution,[status(thm)],[531, 1570])).
% 0.75/0.91 tff(1572,plain,
% 0.75/0.91 (c3_1(a149)),
% 0.75/0.91 inference(unit_resolution,[status(thm)],[246, 1570])).
% 0.75/0.91 tff(1573,plain,
% 0.75/0.91 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a149) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | c1_1(a128) | (~c3_1(a149)) | (~c0_1(a149)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a149) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | c1_1(a128) | (~c3_1(a149)) | (~c0_1(a149)))),
% 0.75/0.91 inference(rewrite,[status(thm)],[])).
% 0.75/0.91 tff(1574,plain,
% 0.75/0.91 (((~ndr1_0) | c1_1(a149) | (~c3_1(a149)) | (~c0_1(a149)) | c3_1(a128) | c0_1(a128) | c2_1(a128) | c2_1(a128) | c1_1(a128) | c0_1(a128)) <=> (c1_1(a149) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | c1_1(a128) | (~c3_1(a149)) | (~c0_1(a149)))),
% 0.75/0.91 inference(rewrite,[status(thm)],[])).
% 0.75/0.91 tff(1575,plain,
% 0.75/0.91 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a149) | (~c3_1(a149)) | (~c0_1(a149)) | c3_1(a128) | c0_1(a128) | c2_1(a128) | c2_1(a128) | c1_1(a128) | c0_1(a128))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a149) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | c1_1(a128) | (~c3_1(a149)) | (~c0_1(a149))))),
% 0.75/0.91 inference(monotonicity,[status(thm)],[1574])).
% 0.75/0.91 tff(1576,plain,
% 0.75/0.91 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a149) | (~c3_1(a149)) | (~c0_1(a149)) | c3_1(a128) | c0_1(a128) | c2_1(a128) | c2_1(a128) | c1_1(a128) | c0_1(a128))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a149) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | c1_1(a128) | (~c3_1(a149)) | (~c0_1(a149)))),
% 0.75/0.91 inference(transitivity,[status(thm)],[1575, 1573])).
% 0.75/0.91 tff(1577,plain,
% 0.75/0.91 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a149) | (~c3_1(a149)) | (~c0_1(a149)) | c3_1(a128) | c0_1(a128) | c2_1(a128) | c2_1(a128) | c1_1(a128) | c0_1(a128))),
% 0.75/0.91 inference(quant_inst,[status(thm)],[])).
% 0.75/0.91 tff(1578,plain,
% 0.75/0.91 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a149) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | c1_1(a128) | (~c3_1(a149)) | (~c0_1(a149))),
% 0.75/0.91 inference(modus_ponens,[status(thm)],[1577, 1576])).
% 0.75/0.91 tff(1579,plain,
% 0.75/0.91 (~c0_1(a149)),
% 0.75/0.91 inference(unit_resolution,[status(thm)],[1578, 175, 1572, 1571, 1493, 1494, 1495, 258, 534])).
% 0.75/0.91 tff(1580,plain,
% 0.75/0.91 (^[V: $i, U: $i] : refl((hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) <=> (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)))),
% 0.75/0.91 inference(bind,[status(th)],[])).
% 0.75/0.91 tff(1581,plain,
% 0.75/0.91 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.75/0.91 inference(quant_intro,[status(thm)],[1580])).
% 0.75/0.91 tff(1582,plain,
% 0.75/0.91 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.75/0.91 inference(rewrite,[status(thm)],[])).
% 0.75/0.91 tff(1583,plain,
% 0.75/0.91 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U))))), (((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)))), (((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | c0_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U))) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c0_1(V))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c0_1(V)))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c0_1(V)) | c1_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V)))), ((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V)) | c3_1(V)))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c1_1(V) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))), ((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)))), (((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp0) <=> (((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) | hskp0))), rewrite((((~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V)) | hskp0) <=> (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))), (((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp0) <=> (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))))),
% 0.75/0.91 inference(bind,[status(th)],[])).
% 0.75/0.91 tff(1584,plain,
% 0.75/0.91 (![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp0) <=> ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.75/0.91 inference(quant_intro,[status(thm)],[1583])).
% 0.75/0.91 tff(1585,axiom,(![V: $i, U: $i] : ((((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c1_1(U)) | c0_1(V)) | c1_1(V)) | c3_1(V)) | hskp0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause159')).
% 0.75/0.91 tff(1586,plain,
% 0.75/0.91 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.75/0.91 inference(modus_ponens,[status(thm)],[1585, 1584])).
% 0.75/0.91 tff(1587,plain,
% 0.75/0.91 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.75/0.91 inference(modus_ponens,[status(thm)],[1586, 1582])).
% 0.75/0.91 tff(1588,plain,(
% 0.75/0.91 ![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.75/0.91 inference(skolemize,[status(sab)],[1587])).
% 0.75/0.91 tff(1589,plain,
% 0.75/0.91 (![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))),
% 0.75/0.91 inference(modus_ponens,[status(thm)],[1588, 1581])).
% 0.75/0.91 tff(1590,plain,
% 0.75/0.91 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c1_1(a149) | c0_1(a128) | c3_1(a128) | (~ndr1_0) | c1_1(a128) | (~c3_1(a149)) | c0_1(a149))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c1_1(a149) | c0_1(a128) | c3_1(a128) | (~ndr1_0) | c1_1(a128) | (~c3_1(a149)) | c0_1(a149))),
% 0.75/0.91 inference(rewrite,[status(thm)],[])).
% 0.75/0.91 tff(1591,plain,
% 0.75/0.91 ((hskp0 | (~ndr1_0) | c1_1(a149) | c0_1(a149) | (~c3_1(a149)) | c3_1(a128) | c1_1(a128) | c0_1(a128)) <=> (hskp0 | c1_1(a149) | c0_1(a128) | c3_1(a128) | (~ndr1_0) | c1_1(a128) | (~c3_1(a149)) | c0_1(a149))),
% 0.75/0.91 inference(rewrite,[status(thm)],[])).
% 0.75/0.91 tff(1592,plain,
% 0.75/0.91 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c1_1(a149) | c0_1(a149) | (~c3_1(a149)) | c3_1(a128) | c1_1(a128) | c0_1(a128))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | c1_1(a149) | c0_1(a128) | c3_1(a128) | (~ndr1_0) | c1_1(a128) | (~c3_1(a149)) | c0_1(a149)))),
% 0.75/0.91 inference(monotonicity,[status(thm)],[1591])).
% 0.75/0.91 tff(1593,plain,
% 0.75/0.91 (((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c1_1(a149) | c0_1(a149) | (~c3_1(a149)) | c3_1(a128) | c1_1(a128) | c0_1(a128))) <=> ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c1_1(a149) | c0_1(a128) | c3_1(a128) | (~ndr1_0) | c1_1(a128) | (~c3_1(a149)) | c0_1(a149))),
% 0.75/0.91 inference(transitivity,[status(thm)],[1592, 1590])).
% 0.75/0.91 tff(1594,plain,
% 0.75/0.91 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | (hskp0 | (~ndr1_0) | c1_1(a149) | c0_1(a149) | (~c3_1(a149)) | c3_1(a128) | c1_1(a128) | c0_1(a128))),
% 0.75/0.91 inference(quant_inst,[status(thm)],[])).
% 0.75/0.91 tff(1595,plain,
% 0.75/0.91 ((~![V: $i, U: $i] : (hskp0 | (~ndr1_0) | c1_1(U) | c0_1(U) | (~c3_1(U)) | c3_1(V) | c1_1(V) | c0_1(V))) | hskp0 | c1_1(a149) | c0_1(a128) | c3_1(a128) | (~ndr1_0) | c1_1(a128) | (~c3_1(a149)) | c0_1(a149)),
% 0.75/0.91 inference(modus_ponens,[status(thm)],[1594, 1593])).
% 0.75/0.91 tff(1596,plain,
% 0.75/0.91 (hskp0),
% 0.75/0.91 inference(unit_resolution,[status(thm)],[1595, 175, 1572, 1571, 1493, 1495, 1589, 534, 1579])).
% 0.75/0.91 tff(1597,plain,
% 0.75/0.91 (((~hskp0) | (~c0_1(a124))) <=> ((~hskp0) | (~c0_1(a124)))),
% 0.75/0.91 inference(rewrite,[status(thm)],[])).
% 0.75/0.91 tff(1598,plain,
% 0.75/0.91 (((~c0_1(a124)) | (~hskp0)) <=> ((~hskp0) | (~c0_1(a124)))),
% 0.75/0.91 inference(rewrite,[status(thm)],[])).
% 0.75/0.91 tff(1599,axiom,((~c0_1(a124)) | (~hskp0)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause129')).
% 0.75/0.91 tff(1600,plain,
% 0.75/0.91 ((~hskp0) | (~c0_1(a124))),
% 0.75/0.91 inference(modus_ponens,[status(thm)],[1599, 1598])).
% 0.75/0.91 tff(1601,plain,
% 0.75/0.91 ((~hskp0) | (~c0_1(a124))),
% 0.75/0.91 inference(modus_ponens,[status(thm)],[1600, 1597])).
% 0.75/0.91 tff(1602,plain,
% 0.75/0.91 (~c0_1(a124)),
% 0.75/0.91 inference(unit_resolution,[status(thm)],[1601, 1596])).
% 0.75/0.91 tff(1603,plain,
% 0.75/0.91 (~c2_1(a149)),
% 0.75/0.91 inference(unit_resolution,[status(thm)],[525, 1570])).
% 0.75/0.91 tff(1604,plain,
% 0.75/0.91 (((~hskp0) | c3_1(a124)) <=> ((~hskp0) | c3_1(a124))),
% 0.75/0.91 inference(rewrite,[status(thm)],[])).
% 0.75/0.91 tff(1605,axiom,((~hskp0) | c3_1(a124)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause83')).
% 0.75/0.91 tff(1606,plain,
% 0.75/0.91 ((~hskp0) | c3_1(a124)),
% 0.75/0.91 inference(modus_ponens,[status(thm)],[1605, 1604])).
% 0.75/0.91 tff(1607,plain,
% 0.75/0.91 ((~hskp0) | c3_1(a124)),
% 0.75/0.91 inference(modus_ponens,[status(thm)],[1606, 1604])).
% 0.75/0.91 tff(1608,plain,
% 0.75/0.91 ((~hskp0) | c3_1(a124)),
% 0.75/0.91 inference(modus_ponens,[status(thm)],[1607, 1604])).
% 0.75/0.91 tff(1609,plain,
% 0.75/0.91 ((~hskp0) | c3_1(a124)),
% 0.75/0.91 inference(modus_ponens,[status(thm)],[1608, 1604])).
% 0.75/0.91 tff(1610,plain,
% 0.75/0.91 ((~hskp0) | c3_1(a124)),
% 0.75/0.91 inference(modus_ponens,[status(thm)],[1609, 1604])).
% 0.75/0.91 tff(1611,plain,
% 0.75/0.91 (c3_1(a124)),
% 0.75/0.91 inference(unit_resolution,[status(thm)],[1610, 1596])).
% 0.75/0.91 tff(1612,plain,
% 0.75/0.91 (((~hskp0) | c2_1(a124)) <=> ((~hskp0) | c2_1(a124))),
% 0.75/0.91 inference(rewrite,[status(thm)],[])).
% 0.75/0.91 tff(1613,axiom,((~hskp0) | c2_1(a124)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause82')).
% 0.75/0.91 tff(1614,plain,
% 0.75/0.91 ((~hskp0) | c2_1(a124)),
% 0.75/0.91 inference(modus_ponens,[status(thm)],[1613, 1612])).
% 0.75/0.91 tff(1615,plain,
% 0.75/0.91 ((~hskp0) | c2_1(a124)),
% 0.75/0.91 inference(modus_ponens,[status(thm)],[1614, 1612])).
% 0.75/0.91 tff(1616,plain,
% 0.75/0.91 ((~hskp0) | c2_1(a124)),
% 0.75/0.91 inference(modus_ponens,[status(thm)],[1615, 1612])).
% 0.75/0.91 tff(1617,plain,
% 0.75/0.91 ((~hskp0) | c2_1(a124)),
% 0.75/0.91 inference(modus_ponens,[status(thm)],[1616, 1612])).
% 0.75/0.91 tff(1618,plain,
% 0.75/0.91 ((~hskp0) | c2_1(a124)),
% 0.75/0.91 inference(modus_ponens,[status(thm)],[1617, 1612])).
% 0.75/0.91 tff(1619,plain,
% 0.75/0.91 (c2_1(a124)),
% 0.75/0.91 inference(unit_resolution,[status(thm)],[1618, 1596])).
% 0.75/0.91 tff(1620,plain,
% 0.75/0.91 (c3_1(a140)),
% 0.75/0.91 inference(unit_resolution,[status(thm)],[604, 1559])).
% 0.75/0.91 tff(1621,plain,
% 0.75/0.91 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | (c1_1(a149) | c2_1(a149) | c0_1(a124) | (~ndr1_0) | (~c2_1(a124)) | (~c3_1(a124)) | c2_1(a140) | (~c3_1(a140)) | (~c1_1(a140)) | (~c3_1(a149)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c1_1(a149) | c2_1(a149) | c0_1(a124) | (~ndr1_0) | (~c2_1(a124)) | (~c3_1(a124)) | c2_1(a140) | (~c3_1(a140)) | (~c1_1(a140)) | (~c3_1(a149)))),
% 0.75/0.91 inference(rewrite,[status(thm)],[])).
% 0.75/0.91 tff(1622,plain,
% 0.75/0.91 (((~ndr1_0) | c2_1(a140) | (~c3_1(a140)) | (~c1_1(a140)) | c1_1(a149) | c2_1(a149) | (~c3_1(a149)) | c0_1(a124) | (~c2_1(a124)) | (~c3_1(a124))) <=> (c1_1(a149) | c2_1(a149) | c0_1(a124) | (~ndr1_0) | (~c2_1(a124)) | (~c3_1(a124)) | c2_1(a140) | (~c3_1(a140)) | (~c1_1(a140)) | (~c3_1(a149)))),
% 0.75/0.91 inference(rewrite,[status(thm)],[])).
% 0.75/0.91 tff(1623,plain,
% 0.75/0.91 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a140) | (~c3_1(a140)) | (~c1_1(a140)) | c1_1(a149) | c2_1(a149) | (~c3_1(a149)) | c0_1(a124) | (~c2_1(a124)) | (~c3_1(a124)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | (c1_1(a149) | c2_1(a149) | c0_1(a124) | (~ndr1_0) | (~c2_1(a124)) | (~c3_1(a124)) | c2_1(a140) | (~c3_1(a140)) | (~c1_1(a140)) | (~c3_1(a149))))),
% 0.75/0.91 inference(monotonicity,[status(thm)],[1622])).
% 0.75/0.91 tff(1624,plain,
% 0.75/0.91 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a140) | (~c3_1(a140)) | (~c1_1(a140)) | c1_1(a149) | c2_1(a149) | (~c3_1(a149)) | c0_1(a124) | (~c2_1(a124)) | (~c3_1(a124)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c1_1(a149) | c2_1(a149) | c0_1(a124) | (~ndr1_0) | (~c2_1(a124)) | (~c3_1(a124)) | c2_1(a140) | (~c3_1(a140)) | (~c1_1(a140)) | (~c3_1(a149)))),
% 0.75/0.91 inference(transitivity,[status(thm)],[1623, 1621])).
% 0.75/0.91 tff(1625,plain,
% 0.75/0.91 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a140) | (~c3_1(a140)) | (~c1_1(a140)) | c1_1(a149) | c2_1(a149) | (~c3_1(a149)) | c0_1(a124) | (~c2_1(a124)) | (~c3_1(a124)))),
% 0.75/0.91 inference(quant_inst,[status(thm)],[])).
% 0.75/0.91 tff(1626,plain,
% 0.75/0.91 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c1_1(a149) | c2_1(a149) | c0_1(a124) | (~ndr1_0) | (~c2_1(a124)) | (~c3_1(a124)) | c2_1(a140) | (~c3_1(a140)) | (~c1_1(a140)) | (~c3_1(a149))),
% 0.75/0.91 inference(modus_ponens,[status(thm)],[1625, 1624])).
% 0.75/0.91 tff(1627,plain,
% 0.75/0.91 ($false),
% 0.75/0.91 inference(unit_resolution,[status(thm)],[1626, 175, 1572, 1561, 1620, 1619, 1611, 1571, 1603, 1602, 214, 1568])).
% 0.75/0.91 tff(1628,plain,(c1_1(a128) | hskp18), inference(lemma,lemma(discharge,[]))).
% 0.75/0.91 tff(1629,plain,
% 0.75/0.91 (c1_1(a128)),
% 0.75/0.91 inference(unit_resolution,[status(thm)],[1628, 95])).
% 0.75/0.91 tff(1630,plain,
% 0.75/0.91 (((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp11 | hskp10 | c0_1(a128) | c2_1(a128) | (~ndr1_0) | (~c1_1(a128)))) <=> ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | hskp11 | hskp10 | c0_1(a128) | c2_1(a128) | (~ndr1_0) | (~c1_1(a128)))),
% 0.75/0.91 inference(rewrite,[status(thm)],[])).
% 0.75/0.91 tff(1631,plain,
% 0.75/0.91 ((hskp11 | hskp10 | (~ndr1_0) | c0_1(a128) | c2_1(a128) | (~c1_1(a128))) <=> (hskp11 | hskp10 | c0_1(a128) | c2_1(a128) | (~ndr1_0) | (~c1_1(a128)))),
% 0.75/0.91 inference(rewrite,[status(thm)],[])).
% 0.75/0.91 tff(1632,plain,
% 0.75/0.91 (((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp11 | hskp10 | (~ndr1_0) | c0_1(a128) | c2_1(a128) | (~c1_1(a128)))) <=> ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp11 | hskp10 | c0_1(a128) | c2_1(a128) | (~ndr1_0) | (~c1_1(a128))))),
% 0.75/0.91 inference(monotonicity,[status(thm)],[1631])).
% 0.75/0.91 tff(1633,plain,
% 0.75/0.91 (((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp11 | hskp10 | (~ndr1_0) | c0_1(a128) | c2_1(a128) | (~c1_1(a128)))) <=> ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | hskp11 | hskp10 | c0_1(a128) | c2_1(a128) | (~ndr1_0) | (~c1_1(a128)))),
% 0.75/0.91 inference(transitivity,[status(thm)],[1632, 1630])).
% 0.75/0.91 tff(1634,plain,
% 0.75/0.91 ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | (hskp11 | hskp10 | (~ndr1_0) | c0_1(a128) | c2_1(a128) | (~c1_1(a128)))),
% 0.75/0.91 inference(quant_inst,[status(thm)],[])).
% 0.75/0.91 tff(1635,plain,
% 0.75/0.91 ((~![U: $i] : (hskp11 | hskp10 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c1_1(U)))) | hskp11 | hskp10 | c0_1(a128) | c2_1(a128) | (~ndr1_0) | (~c1_1(a128))),
% 0.75/0.91 inference(modus_ponens,[status(thm)],[1634, 1633])).
% 0.75/0.91 tff(1636,plain,
% 0.75/0.91 (hskp11 | (~c1_1(a128))),
% 0.75/0.91 inference(unit_resolution,[status(thm)],[1635, 175, 1185, 1493, 1494, 1379])).
% 0.75/0.91 tff(1637,plain,
% 0.75/0.91 (hskp11),
% 0.75/0.91 inference(unit_resolution,[status(thm)],[1636, 1629])).
% 0.75/0.91 tff(1638,plain,
% 0.75/0.91 (~c3_1(a139)),
% 0.75/0.91 inference(unit_resolution,[status(thm)],[1407, 1637])).
% 0.75/0.91 tff(1639,plain,
% 0.75/0.91 (~c1_1(a139)),
% 0.75/0.91 inference(unit_resolution,[status(thm)],[1413, 1637])).
% 0.75/0.91 tff(1640,plain,
% 0.75/0.91 (^[V: $i, U: $i] : refl((hskp16 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) <=> (hskp16 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))))),
% 0.75/0.91 inference(bind,[status(th)],[])).
% 0.75/0.91 tff(1641,plain,
% 0.75/0.91 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.75/0.91 inference(quant_intro,[status(thm)],[1640])).
% 0.75/0.91 tff(1642,plain,
% 0.75/0.91 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.75/0.91 inference(rewrite,[status(thm)],[])).
% 0.75/0.91 tff(1643,plain,
% 0.75/0.91 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> (((~ndr1_0) | (~c1_1(U))) | (~c2_1(V))))), rewrite((((~ndr1_0) | (~c1_1(U))) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(V)))), ((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) <=> ((~ndr1_0) | (~c1_1(U)) | (~c2_1(V))))), (((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) <=> (((~ndr1_0) | (~c1_1(U)) | (~c2_1(V))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c2_1(V)))), (((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c2_1(V))))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c2_1(V))) | c3_1(U)))), rewrite((((~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c2_1(V))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | (~c2_1(V)))), ((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | (~c2_1(V))))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | (~c2_1(V))) | c0_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | (~c2_1(V))) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V)))), (((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V))))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V))) | c3_1(V)))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c0_1(V) | (~c2_1(V))) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))), ((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) <=> ((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp16) <=> (((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) | hskp16))), rewrite((((~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V))) | hskp16) <=> (hskp16 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))), (((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp16) <=> (hskp16 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))))),
% 0.75/0.91 inference(bind,[status(th)],[])).
% 0.75/0.91 tff(1644,plain,
% 0.75/0.91 (![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp16) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.75/0.91 inference(quant_intro,[status(thm)],[1643])).
% 0.75/0.91 tff(1645,axiom,(![V: $i, U: $i] : ((((((((~c1_1(U)) | (~ndr1_0)) | (~c2_1(V))) | c2_1(U)) | c3_1(U)) | c0_1(V)) | c3_1(V)) | hskp16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause163')).
% 0.75/0.91 tff(1646,plain,
% 0.75/0.91 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.75/0.91 inference(modus_ponens,[status(thm)],[1645, 1644])).
% 0.75/0.91 tff(1647,plain,
% 0.75/0.91 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.75/0.91 inference(modus_ponens,[status(thm)],[1646, 1642])).
% 0.75/0.91 tff(1648,plain,(
% 0.75/0.91 ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.75/0.91 inference(skolemize,[status(sab)],[1647])).
% 0.75/0.91 tff(1649,plain,
% 0.75/0.91 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))),
% 0.75/0.92 inference(modus_ponens,[status(thm)],[1648, 1641])).
% 0.75/0.92 tff(1650,plain,
% 0.75/0.92 (hskp21 | (~c1_1(a128))),
% 0.75/0.92 inference(unit_resolution,[status(thm)],[284, 175, 95, 1494, 1495, 128])).
% 0.75/0.92 tff(1651,plain,
% 0.75/0.92 (hskp21),
% 0.75/0.92 inference(unit_resolution,[status(thm)],[1650, 1629])).
% 0.75/0.92 tff(1652,plain,
% 0.75/0.92 (~c2_1(a170)),
% 0.75/0.92 inference(unit_resolution,[status(thm)],[291, 1651])).
% 0.75/0.92 tff(1653,plain,
% 0.75/0.92 (~c0_1(a170)),
% 0.75/0.92 inference(unit_resolution,[status(thm)],[297, 1651])).
% 0.75/0.92 tff(1654,plain,
% 0.75/0.92 (c3_1(a170)),
% 0.75/0.92 inference(unit_resolution,[status(thm)],[322, 1651])).
% 0.75/0.92 tff(1655,plain,
% 0.75/0.92 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | c0_1(a170) | c2_1(a170) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c3_1(a170)))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp9 | c0_1(a170) | c2_1(a170) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c3_1(a170)))),
% 0.75/0.92 inference(rewrite,[status(thm)],[])).
% 0.75/0.92 tff(1656,plain,
% 0.75/0.92 ((hskp9 | (~ndr1_0) | c0_1(a170) | c2_1(a170) | (~c3_1(a170)) | c3_1(a128) | c0_1(a128) | c2_1(a128)) <=> (hskp9 | c0_1(a170) | c2_1(a170) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c3_1(a170)))),
% 0.75/0.92 inference(rewrite,[status(thm)],[])).
% 0.75/0.92 tff(1657,plain,
% 0.75/0.92 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | (~ndr1_0) | c0_1(a170) | c2_1(a170) | (~c3_1(a170)) | c3_1(a128) | c0_1(a128) | c2_1(a128))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | c0_1(a170) | c2_1(a170) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c3_1(a170))))),
% 0.75/0.92 inference(monotonicity,[status(thm)],[1656])).
% 0.75/0.92 tff(1658,plain,
% 0.75/0.92 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | (~ndr1_0) | c0_1(a170) | c2_1(a170) | (~c3_1(a170)) | c3_1(a128) | c0_1(a128) | c2_1(a128))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp9 | c0_1(a170) | c2_1(a170) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c3_1(a170)))),
% 0.75/0.92 inference(transitivity,[status(thm)],[1657, 1655])).
% 0.75/0.92 tff(1659,plain,
% 0.75/0.92 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | (~ndr1_0) | c0_1(a170) | c2_1(a170) | (~c3_1(a170)) | c3_1(a128) | c0_1(a128) | c2_1(a128))),
% 0.75/0.92 inference(quant_inst,[status(thm)],[])).
% 0.75/0.92 tff(1660,plain,
% 0.75/0.92 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp9 | c0_1(a170) | c2_1(a170) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c3_1(a170))),
% 0.75/0.92 inference(modus_ponens,[status(thm)],[1659, 1658])).
% 0.75/0.92 tff(1661,plain,
% 0.75/0.92 (hskp9),
% 0.75/0.92 inference(unit_resolution,[status(thm)],[1660, 175, 1654, 1653, 1652, 1493, 1494, 1495, 31])).
% 0.75/0.92 tff(1662,plain,
% 0.75/0.92 (c0_1(a136)),
% 0.75/0.92 inference(unit_resolution,[status(thm)],[783, 1661])).
% 0.75/0.92 tff(1663,plain,
% 0.75/0.92 (~c3_1(a136)),
% 0.75/0.92 inference(unit_resolution,[status(thm)],[759, 1661])).
% 0.75/0.92 tff(1664,plain,
% 0.75/0.92 (c2_1(a136)),
% 0.75/0.92 inference(unit_resolution,[status(thm)],[767, 1661])).
% 0.75/0.92 tff(1665,plain,
% 0.75/0.92 (^[U: $i] : refl((hskp13 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> (hskp13 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))))),
% 0.75/0.92 inference(bind,[status(th)],[])).
% 0.75/0.92 tff(1666,plain,
% 0.75/0.92 (![U: $i] : (hskp13 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp13 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.75/0.92 inference(quant_intro,[status(thm)],[1665])).
% 0.75/0.92 tff(1667,plain,
% 0.75/0.92 (![U: $i] : (hskp13 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp13 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.75/0.92 inference(rewrite,[status(thm)],[])).
% 0.75/0.92 tff(1668,plain,
% 0.75/0.92 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp10) <=> (((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp10))), rewrite((((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp10) <=> (hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp10) <=> (hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp10) | hskp13) <=> ((hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp13))), rewrite(((hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp13) <=> (hskp13 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp10) | hskp13) <=> (hskp13 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))))),
% 0.75/0.92 inference(bind,[status(th)],[])).
% 0.75/0.92 tff(1669,plain,
% 0.75/0.92 (![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp10) | hskp13) <=> ![U: $i] : (hskp13 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.75/0.92 inference(quant_intro,[status(thm)],[1668])).
% 0.75/0.92 tff(1670,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c1_1(U)) | hskp10) | hskp13)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause150')).
% 0.75/0.92 tff(1671,plain,
% 0.75/0.92 (![U: $i] : (hskp13 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.75/0.92 inference(modus_ponens,[status(thm)],[1670, 1669])).
% 0.75/0.92 tff(1672,plain,
% 0.75/0.92 (![U: $i] : (hskp13 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.75/0.92 inference(modus_ponens,[status(thm)],[1671, 1667])).
% 0.75/0.92 tff(1673,plain,(
% 0.75/0.92 ![U: $i] : (hskp13 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.75/0.92 inference(skolemize,[status(sab)],[1672])).
% 0.75/0.92 tff(1674,plain,
% 0.75/0.92 (![U: $i] : (hskp13 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.75/0.92 inference(modus_ponens,[status(thm)],[1673, 1666])).
% 0.75/0.92 tff(1675,plain,
% 0.75/0.92 (^[U: $i] : refl((hskp28 | hskp13 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U))) <=> (hskp28 | hskp13 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U))))),
% 0.75/0.92 inference(bind,[status(th)],[])).
% 0.75/0.92 tff(1676,plain,
% 0.75/0.92 (![U: $i] : (hskp28 | hskp13 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp28 | hskp13 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))),
% 0.75/0.92 inference(quant_intro,[status(thm)],[1675])).
% 0.75/0.92 tff(1677,plain,
% 0.75/0.92 (![U: $i] : (hskp28 | hskp13 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U))) <=> ![U: $i] : (hskp28 | hskp13 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))),
% 0.75/0.92 inference(rewrite,[status(thm)],[])).
% 0.75/0.92 tff(1678,plain,
% 0.75/0.92 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c3_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c3_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U)))), ((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c3_1(U))))), (((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c3_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c3_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))), (((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) <=> ((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U))))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp28) <=> (((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U))) | hskp28))), rewrite((((~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U))) | hskp28) <=> (hskp28 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))), ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp28) <=> (hskp28 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U))))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp28) | hskp13) <=> ((hskp28 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U))) | hskp13))), rewrite(((hskp28 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U))) | hskp13) <=> (hskp28 | hskp13 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))), (((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp28) | hskp13) <=> (hskp28 | hskp13 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))))),
% 0.75/0.92 inference(bind,[status(th)],[])).
% 0.75/0.92 tff(1679,plain,
% 0.75/0.92 (![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp28) | hskp13) <=> ![U: $i] : (hskp28 | hskp13 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))),
% 0.75/0.92 inference(quant_intro,[status(thm)],[1678])).
% 0.75/0.92 tff(1680,axiom,(![U: $i] : ((((((~c3_1(U)) | (~ndr1_0)) | c0_1(U)) | c2_1(U)) | hskp28) | hskp13)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause137')).
% 0.75/0.92 tff(1681,plain,
% 0.75/0.92 (![U: $i] : (hskp28 | hskp13 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))),
% 0.75/0.92 inference(modus_ponens,[status(thm)],[1680, 1679])).
% 0.75/0.92 tff(1682,plain,
% 0.75/0.92 (![U: $i] : (hskp28 | hskp13 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))),
% 0.75/0.92 inference(modus_ponens,[status(thm)],[1681, 1677])).
% 0.75/0.92 tff(1683,plain,(
% 0.75/0.92 ![U: $i] : (hskp28 | hskp13 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))),
% 0.75/0.92 inference(skolemize,[status(sab)],[1682])).
% 0.75/0.92 tff(1684,plain,
% 0.75/0.92 (![U: $i] : (hskp28 | hskp13 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))),
% 0.75/0.92 inference(modus_ponens,[status(thm)],[1683, 1676])).
% 0.75/0.92 tff(1685,assumption,(c3_1(a170)), introduced(assumption)).
% 0.75/0.92 tff(1686,plain,
% 0.75/0.92 (((~![U: $i] : (hskp28 | hskp13 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp28 | hskp13 | c0_1(a170) | c2_1(a170) | (~ndr1_0) | (~c3_1(a170)))) <=> ((~![U: $i] : (hskp28 | hskp13 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | hskp28 | hskp13 | c0_1(a170) | c2_1(a170) | (~ndr1_0) | (~c3_1(a170)))),
% 0.75/0.92 inference(rewrite,[status(thm)],[])).
% 0.75/0.92 tff(1687,plain,
% 0.75/0.92 ((hskp28 | hskp13 | (~ndr1_0) | c0_1(a170) | c2_1(a170) | (~c3_1(a170))) <=> (hskp28 | hskp13 | c0_1(a170) | c2_1(a170) | (~ndr1_0) | (~c3_1(a170)))),
% 0.75/0.92 inference(rewrite,[status(thm)],[])).
% 0.75/0.92 tff(1688,plain,
% 0.75/0.92 (((~![U: $i] : (hskp28 | hskp13 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp28 | hskp13 | (~ndr1_0) | c0_1(a170) | c2_1(a170) | (~c3_1(a170)))) <=> ((~![U: $i] : (hskp28 | hskp13 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp28 | hskp13 | c0_1(a170) | c2_1(a170) | (~ndr1_0) | (~c3_1(a170))))),
% 0.75/0.92 inference(monotonicity,[status(thm)],[1687])).
% 0.75/0.92 tff(1689,plain,
% 0.75/0.92 (((~![U: $i] : (hskp28 | hskp13 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp28 | hskp13 | (~ndr1_0) | c0_1(a170) | c2_1(a170) | (~c3_1(a170)))) <=> ((~![U: $i] : (hskp28 | hskp13 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | hskp28 | hskp13 | c0_1(a170) | c2_1(a170) | (~ndr1_0) | (~c3_1(a170)))),
% 0.75/0.92 inference(transitivity,[status(thm)],[1688, 1686])).
% 0.75/0.92 tff(1690,plain,
% 0.75/0.92 ((~![U: $i] : (hskp28 | hskp13 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | (hskp28 | hskp13 | (~ndr1_0) | c0_1(a170) | c2_1(a170) | (~c3_1(a170)))),
% 0.75/0.92 inference(quant_inst,[status(thm)],[])).
% 0.75/0.92 tff(1691,plain,
% 0.75/0.92 ((~![U: $i] : (hskp28 | hskp13 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)))) | hskp28 | hskp13 | c0_1(a170) | c2_1(a170) | (~ndr1_0) | (~c3_1(a170))),
% 0.75/0.92 inference(modus_ponens,[status(thm)],[1690, 1689])).
% 0.75/0.92 tff(1692,plain,
% 0.75/0.92 (hskp28 | hskp13),
% 0.75/0.92 inference(unit_resolution,[status(thm)],[1691, 175, 1685, 439, 438, 1684])).
% 0.75/0.92 tff(1693,plain,
% 0.75/0.92 (hskp28),
% 0.75/0.92 inference(unit_resolution,[status(thm)],[1692, 11])).
% 0.75/0.92 tff(1694,plain,
% 0.75/0.92 (((~hskp28) | c3_1(a143)) <=> ((~hskp28) | c3_1(a143))),
% 0.75/0.92 inference(rewrite,[status(thm)],[])).
% 0.75/0.92 tff(1695,axiom,((~hskp28) | c3_1(a143)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause45')).
% 0.75/0.92 tff(1696,plain,
% 0.75/0.92 ((~hskp28) | c3_1(a143)),
% 0.75/0.92 inference(modus_ponens,[status(thm)],[1695, 1694])).
% 0.75/0.92 tff(1697,plain,
% 0.75/0.92 ((~hskp28) | c3_1(a143)),
% 0.75/0.92 inference(modus_ponens,[status(thm)],[1696, 1694])).
% 0.75/0.92 tff(1698,plain,
% 0.75/0.92 ((~hskp28) | c3_1(a143)),
% 0.75/0.92 inference(modus_ponens,[status(thm)],[1697, 1694])).
% 0.75/0.92 tff(1699,plain,
% 0.75/0.92 ((~hskp28) | c3_1(a143)),
% 0.75/0.92 inference(modus_ponens,[status(thm)],[1698, 1694])).
% 0.75/0.92 tff(1700,plain,
% 0.75/0.92 ((~hskp28) | c3_1(a143)),
% 0.75/0.92 inference(modus_ponens,[status(thm)],[1699, 1694])).
% 0.75/0.92 tff(1701,plain,
% 0.75/0.92 (c3_1(a143)),
% 0.75/0.92 inference(unit_resolution,[status(thm)],[1700, 1693])).
% 0.75/0.92 tff(1702,plain,
% 0.75/0.92 (((~hskp28) | c0_1(a143)) <=> ((~hskp28) | c0_1(a143))),
% 0.75/0.92 inference(rewrite,[status(thm)],[])).
% 0.75/0.92 tff(1703,axiom,((~hskp28) | c0_1(a143)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause43')).
% 0.75/0.92 tff(1704,plain,
% 0.75/0.92 ((~hskp28) | c0_1(a143)),
% 0.75/0.92 inference(modus_ponens,[status(thm)],[1703, 1702])).
% 0.75/0.92 tff(1705,plain,
% 0.75/0.92 ((~hskp28) | c0_1(a143)),
% 0.75/0.92 inference(modus_ponens,[status(thm)],[1704, 1702])).
% 0.75/0.92 tff(1706,plain,
% 0.75/0.92 ((~hskp28) | c0_1(a143)),
% 0.75/0.92 inference(modus_ponens,[status(thm)],[1705, 1702])).
% 0.75/0.92 tff(1707,plain,
% 0.75/0.92 ((~hskp28) | c0_1(a143)),
% 0.75/0.92 inference(modus_ponens,[status(thm)],[1706, 1702])).
% 0.75/0.92 tff(1708,plain,
% 0.75/0.92 ((~hskp28) | c0_1(a143)),
% 0.75/0.92 inference(modus_ponens,[status(thm)],[1707, 1702])).
% 0.75/0.92 tff(1709,plain,
% 0.75/0.92 (c0_1(a143)),
% 0.75/0.92 inference(unit_resolution,[status(thm)],[1708, 1693])).
% 0.75/0.92 tff(1710,plain,
% 0.75/0.92 (((~![U: $i] : (hskp13 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp13 | hskp10 | (~ndr1_0) | c1_1(a143) | (~c0_1(a143)) | (~c3_1(a143)))) <=> ((~![U: $i] : (hskp13 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp13 | hskp10 | (~ndr1_0) | c1_1(a143) | (~c0_1(a143)) | (~c3_1(a143)))),
% 0.75/0.92 inference(rewrite,[status(thm)],[])).
% 0.75/0.92 tff(1711,plain,
% 0.75/0.92 ((hskp13 | hskp10 | (~ndr1_0) | c1_1(a143) | (~c3_1(a143)) | (~c0_1(a143))) <=> (hskp13 | hskp10 | (~ndr1_0) | c1_1(a143) | (~c0_1(a143)) | (~c3_1(a143)))),
% 0.75/0.92 inference(rewrite,[status(thm)],[])).
% 0.75/0.92 tff(1712,plain,
% 0.75/0.92 (((~![U: $i] : (hskp13 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp13 | hskp10 | (~ndr1_0) | c1_1(a143) | (~c3_1(a143)) | (~c0_1(a143)))) <=> ((~![U: $i] : (hskp13 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp13 | hskp10 | (~ndr1_0) | c1_1(a143) | (~c0_1(a143)) | (~c3_1(a143))))),
% 0.75/0.92 inference(monotonicity,[status(thm)],[1711])).
% 0.75/0.92 tff(1713,plain,
% 0.75/0.92 (((~![U: $i] : (hskp13 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp13 | hskp10 | (~ndr1_0) | c1_1(a143) | (~c3_1(a143)) | (~c0_1(a143)))) <=> ((~![U: $i] : (hskp13 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp13 | hskp10 | (~ndr1_0) | c1_1(a143) | (~c0_1(a143)) | (~c3_1(a143)))),
% 0.75/0.92 inference(transitivity,[status(thm)],[1712, 1710])).
% 0.75/0.92 tff(1714,plain,
% 0.75/0.92 ((~![U: $i] : (hskp13 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp13 | hskp10 | (~ndr1_0) | c1_1(a143) | (~c3_1(a143)) | (~c0_1(a143)))),
% 0.75/0.92 inference(quant_inst,[status(thm)],[])).
% 0.75/0.92 tff(1715,plain,
% 0.75/0.92 ((~![U: $i] : (hskp13 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp13 | hskp10 | (~ndr1_0) | c1_1(a143) | (~c0_1(a143)) | (~c3_1(a143))),
% 0.75/0.92 inference(modus_ponens,[status(thm)],[1714, 1713])).
% 0.75/0.92 tff(1716,plain,
% 0.75/0.92 (c1_1(a143)),
% 0.75/0.92 inference(unit_resolution,[status(thm)],[1715, 175, 11, 1223, 1709, 1701, 1674])).
% 0.75/0.92 tff(1717,plain,
% 0.75/0.92 (^[U: $i] : refl((hskp19 | hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) <=> (hskp19 | hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))))),
% 0.75/0.92 inference(bind,[status(th)],[])).
% 0.75/0.92 tff(1718,plain,
% 0.75/0.92 (![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.75/0.92 inference(quant_intro,[status(thm)],[1717])).
% 0.75/0.92 tff(1719,plain,
% 0.75/0.92 (![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.75/0.92 inference(rewrite,[status(thm)],[])).
% 0.75/0.92 tff(1720,plain,
% 0.75/0.92 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) <=> ((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp19) <=> (((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp19))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp19) <=> (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp19) <=> (hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp19) | hskp13) <=> ((hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp13))), rewrite(((hskp19 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U))) | hskp13) <=> (hskp19 | hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp19) | hskp13) <=> (hskp19 | hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))))),
% 0.75/0.92 inference(bind,[status(th)],[])).
% 0.75/0.92 tff(1721,plain,
% 0.75/0.92 (![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp19) | hskp13) <=> ![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.75/0.92 inference(quant_intro,[status(thm)],[1720])).
% 0.75/0.92 tff(1722,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c1_1(U))) | (~c2_1(U))) | (~ndr1_0)) | hskp19) | hskp13)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause154')).
% 0.75/0.92 tff(1723,plain,
% 0.75/0.92 (![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.75/0.92 inference(modus_ponens,[status(thm)],[1722, 1721])).
% 0.75/0.92 tff(1724,plain,
% 0.75/0.92 (![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.75/0.92 inference(modus_ponens,[status(thm)],[1723, 1719])).
% 0.75/0.92 tff(1725,plain,(
% 0.75/0.92 ![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.75/0.92 inference(skolemize,[status(sab)],[1724])).
% 0.75/0.92 tff(1726,plain,
% 0.75/0.92 (![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))),
% 0.75/0.92 inference(modus_ponens,[status(thm)],[1725, 1718])).
% 0.75/0.92 tff(1727,plain,
% 0.75/0.92 (((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp19 | hskp13 | (~ndr1_0) | (~c2_1(a199)) | (~c0_1(a199)) | (~c1_1(a199)))) <=> ((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp19 | hskp13 | (~ndr1_0) | (~c2_1(a199)) | (~c0_1(a199)) | (~c1_1(a199)))),
% 0.75/0.92 inference(rewrite,[status(thm)],[])).
% 0.75/0.92 tff(1728,plain,
% 0.75/0.92 ((hskp19 | hskp13 | (~ndr1_0) | (~c2_1(a199)) | (~c1_1(a199)) | (~c0_1(a199))) <=> (hskp19 | hskp13 | (~ndr1_0) | (~c2_1(a199)) | (~c0_1(a199)) | (~c1_1(a199)))),
% 0.75/0.92 inference(rewrite,[status(thm)],[])).
% 0.75/0.92 tff(1729,plain,
% 0.75/0.92 (((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp19 | hskp13 | (~ndr1_0) | (~c2_1(a199)) | (~c1_1(a199)) | (~c0_1(a199)))) <=> ((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp19 | hskp13 | (~ndr1_0) | (~c2_1(a199)) | (~c0_1(a199)) | (~c1_1(a199))))),
% 0.75/0.92 inference(monotonicity,[status(thm)],[1728])).
% 0.75/0.92 tff(1730,plain,
% 0.75/0.92 (((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp19 | hskp13 | (~ndr1_0) | (~c2_1(a199)) | (~c1_1(a199)) | (~c0_1(a199)))) <=> ((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp19 | hskp13 | (~ndr1_0) | (~c2_1(a199)) | (~c0_1(a199)) | (~c1_1(a199)))),
% 0.75/0.92 inference(transitivity,[status(thm)],[1729, 1727])).
% 0.75/0.92 tff(1731,plain,
% 0.75/0.92 ((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | (hskp19 | hskp13 | (~ndr1_0) | (~c2_1(a199)) | (~c1_1(a199)) | (~c0_1(a199)))),
% 0.75/0.92 inference(quant_inst,[status(thm)],[])).
% 0.75/0.92 tff(1732,plain,
% 0.75/0.92 ((~![U: $i] : (hskp19 | hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)))) | hskp19 | hskp13 | (~ndr1_0) | (~c2_1(a199)) | (~c0_1(a199)) | (~c1_1(a199))),
% 0.75/0.92 inference(modus_ponens,[status(thm)],[1731, 1730])).
% 0.75/0.92 tff(1733,plain,
% 0.75/0.92 (hskp19 | hskp13),
% 0.75/0.92 inference(unit_resolution,[status(thm)],[1732, 175, 1222, 1221, 1232, 1726])).
% 0.75/0.92 tff(1734,plain,
% 0.75/0.92 (hskp19),
% 0.75/0.92 inference(unit_resolution,[status(thm)],[1733, 11])).
% 0.75/0.92 tff(1735,plain,
% 0.75/0.92 (c3_1(a162)),
% 0.75/0.92 inference(unit_resolution,[status(thm)],[390, 1734])).
% 0.75/0.92 tff(1736,plain,
% 0.75/0.92 (c0_1(a162)),
% 0.75/0.92 inference(unit_resolution,[status(thm)],[398, 1734])).
% 0.75/0.92 tff(1737,plain,
% 0.75/0.92 (((~![U: $i] : (hskp13 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp13 | hskp10 | (~ndr1_0) | (~c3_1(a162)) | c1_1(a162) | (~c0_1(a162)))) <=> ((~![U: $i] : (hskp13 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp13 | hskp10 | (~ndr1_0) | (~c3_1(a162)) | c1_1(a162) | (~c0_1(a162)))),
% 0.75/0.92 inference(rewrite,[status(thm)],[])).
% 0.75/0.92 tff(1738,plain,
% 0.75/0.92 ((hskp13 | hskp10 | (~ndr1_0) | c1_1(a162) | (~c3_1(a162)) | (~c0_1(a162))) <=> (hskp13 | hskp10 | (~ndr1_0) | (~c3_1(a162)) | c1_1(a162) | (~c0_1(a162)))),
% 0.75/0.92 inference(rewrite,[status(thm)],[])).
% 0.75/0.92 tff(1739,plain,
% 0.75/0.92 (((~![U: $i] : (hskp13 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp13 | hskp10 | (~ndr1_0) | c1_1(a162) | (~c3_1(a162)) | (~c0_1(a162)))) <=> ((~![U: $i] : (hskp13 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp13 | hskp10 | (~ndr1_0) | (~c3_1(a162)) | c1_1(a162) | (~c0_1(a162))))),
% 0.75/0.92 inference(monotonicity,[status(thm)],[1738])).
% 0.75/0.92 tff(1740,plain,
% 0.75/0.92 (((~![U: $i] : (hskp13 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp13 | hskp10 | (~ndr1_0) | c1_1(a162) | (~c3_1(a162)) | (~c0_1(a162)))) <=> ((~![U: $i] : (hskp13 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp13 | hskp10 | (~ndr1_0) | (~c3_1(a162)) | c1_1(a162) | (~c0_1(a162)))),
% 0.75/0.92 inference(transitivity,[status(thm)],[1739, 1737])).
% 0.75/0.92 tff(1741,plain,
% 0.75/0.92 ((~![U: $i] : (hskp13 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp13 | hskp10 | (~ndr1_0) | c1_1(a162) | (~c3_1(a162)) | (~c0_1(a162)))),
% 0.75/0.92 inference(quant_inst,[status(thm)],[])).
% 0.75/0.92 tff(1742,plain,
% 0.75/0.92 ((~![U: $i] : (hskp13 | hskp10 | (~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp13 | hskp10 | (~ndr1_0) | (~c3_1(a162)) | c1_1(a162) | (~c0_1(a162))),
% 0.75/0.92 inference(modus_ponens,[status(thm)],[1741, 1740])).
% 0.75/0.92 tff(1743,plain,
% 0.75/0.92 (c1_1(a162)),
% 0.75/0.92 inference(unit_resolution,[status(thm)],[1742, 175, 11, 1223, 1736, 1735, 1674])).
% 0.75/0.92 tff(1744,plain,
% 0.75/0.92 (hskp13 | (~c1_1(a136))),
% 0.75/0.92 inference(unit_resolution,[status(thm)],[1337, 175, 1054, 1053, 1065, 21])).
% 0.75/0.92 tff(1745,plain,
% 0.75/0.92 (~c1_1(a136)),
% 0.75/0.92 inference(unit_resolution,[status(thm)],[1744, 11])).
% 0.75/0.92 tff(1746,plain,
% 0.75/0.92 (~c2_1(a162)),
% 0.75/0.92 inference(unit_resolution,[status(thm)],[382, 1734])).
% 0.75/0.92 tff(1747,plain,
% 0.75/0.92 (((~hskp28) | c2_1(a143)) <=> ((~hskp28) | c2_1(a143))),
% 0.75/0.92 inference(rewrite,[status(thm)],[])).
% 0.75/0.92 tff(1748,axiom,((~hskp28) | c2_1(a143)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause44')).
% 0.75/0.92 tff(1749,plain,
% 0.75/0.92 ((~hskp28) | c2_1(a143)),
% 0.75/0.92 inference(modus_ponens,[status(thm)],[1748, 1747])).
% 0.75/0.92 tff(1750,plain,
% 0.75/0.92 ((~hskp28) | c2_1(a143)),
% 0.75/0.92 inference(modus_ponens,[status(thm)],[1749, 1747])).
% 0.75/0.92 tff(1751,plain,
% 0.75/0.92 ((~hskp28) | c2_1(a143)),
% 0.75/0.92 inference(modus_ponens,[status(thm)],[1750, 1747])).
% 0.75/0.92 tff(1752,plain,
% 0.75/0.92 ((~hskp28) | c2_1(a143)),
% 0.75/0.92 inference(modus_ponens,[status(thm)],[1751, 1747])).
% 0.75/0.92 tff(1753,plain,
% 0.75/0.92 ((~hskp28) | c2_1(a143)),
% 0.75/0.92 inference(modus_ponens,[status(thm)],[1752, 1747])).
% 0.75/0.92 tff(1754,plain,
% 0.75/0.92 (c2_1(a143)),
% 0.75/0.92 inference(unit_resolution,[status(thm)],[1753, 1693])).
% 0.75/0.92 tff(1755,plain,
% 0.75/0.92 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | (c2_1(a162) | c3_1(a136) | (~ndr1_0) | (~c1_1(a143)) | (~c3_1(a143)) | (~c2_1(a143)) | c1_1(a136) | (~c2_1(a136)) | (~c1_1(a162)) | (~c0_1(a162)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | c2_1(a162) | c3_1(a136) | (~ndr1_0) | (~c1_1(a143)) | (~c3_1(a143)) | (~c2_1(a143)) | c1_1(a136) | (~c2_1(a136)) | (~c1_1(a162)) | (~c0_1(a162)))),
% 0.75/0.92 inference(rewrite,[status(thm)],[])).
% 0.75/0.92 tff(1756,plain,
% 0.75/0.92 (((~ndr1_0) | (~c2_1(a143)) | (~c3_1(a143)) | (~c1_1(a143)) | c2_1(a162) | (~c1_1(a162)) | (~c0_1(a162)) | c1_1(a136) | c3_1(a136) | (~c2_1(a136))) <=> (c2_1(a162) | c3_1(a136) | (~ndr1_0) | (~c1_1(a143)) | (~c3_1(a143)) | (~c2_1(a143)) | c1_1(a136) | (~c2_1(a136)) | (~c1_1(a162)) | (~c0_1(a162)))),
% 0.75/0.92 inference(rewrite,[status(thm)],[])).
% 0.75/0.92 tff(1757,plain,
% 0.75/0.92 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a143)) | (~c3_1(a143)) | (~c1_1(a143)) | c2_1(a162) | (~c1_1(a162)) | (~c0_1(a162)) | c1_1(a136) | c3_1(a136) | (~c2_1(a136)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | (c2_1(a162) | c3_1(a136) | (~ndr1_0) | (~c1_1(a143)) | (~c3_1(a143)) | (~c2_1(a143)) | c1_1(a136) | (~c2_1(a136)) | (~c1_1(a162)) | (~c0_1(a162))))),
% 0.75/0.92 inference(monotonicity,[status(thm)],[1756])).
% 0.75/0.92 tff(1758,plain,
% 0.75/0.92 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a143)) | (~c3_1(a143)) | (~c1_1(a143)) | c2_1(a162) | (~c1_1(a162)) | (~c0_1(a162)) | c1_1(a136) | c3_1(a136) | (~c2_1(a136)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | c2_1(a162) | c3_1(a136) | (~ndr1_0) | (~c1_1(a143)) | (~c3_1(a143)) | (~c2_1(a143)) | c1_1(a136) | (~c2_1(a136)) | (~c1_1(a162)) | (~c0_1(a162)))),
% 0.75/0.92 inference(transitivity,[status(thm)],[1757, 1755])).
% 0.75/0.92 tff(1759,plain,
% 0.75/0.92 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a143)) | (~c3_1(a143)) | (~c1_1(a143)) | c2_1(a162) | (~c1_1(a162)) | (~c0_1(a162)) | c1_1(a136) | c3_1(a136) | (~c2_1(a136)))),
% 0.75/0.92 inference(quant_inst,[status(thm)],[])).
% 0.75/0.92 tff(1760,plain,
% 0.75/0.92 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | c2_1(a162) | c3_1(a136) | (~ndr1_0) | (~c1_1(a143)) | (~c3_1(a143)) | (~c2_1(a143)) | c1_1(a136) | (~c2_1(a136)) | (~c1_1(a162)) | (~c0_1(a162))),
% 0.75/0.92 inference(modus_ponens,[status(thm)],[1759, 1758])).
% 0.75/0.92 tff(1761,plain,
% 0.75/0.92 ($false),
% 0.75/0.92 inference(unit_resolution,[status(thm)],[1760, 175, 1754, 1701, 1736, 1053, 1746, 1065, 94, 1745, 1743, 1716])).
% 0.75/0.92 tff(1762,plain,(hskp13 | (~c2_1(a136)) | c3_1(a136) | hskp10 | (~c0_1(a136)) | (~c3_1(a170)) | c0_1(a170) | c2_1(a170) | (~c0_1(a199)) | (~c1_1(a199)) | (~c2_1(a199))), inference(lemma,lemma(discharge,[]))).
% 0.75/0.92 tff(1763,plain,
% 0.75/0.92 (hskp13),
% 0.75/0.92 inference(unit_resolution,[status(thm)],[1762, 1664, 1663, 1185, 1662, 1654, 1653, 1652, 1210, 1202, 1194])).
% 0.75/0.92 tff(1764,plain,
% 0.75/0.92 (~c3_1(a144)),
% 0.75/0.92 inference(unit_resolution,[status(thm)],[928, 1763])).
% 0.75/0.92 tff(1765,plain,
% 0.75/0.92 (~c0_1(a144)),
% 0.75/0.92 inference(unit_resolution,[status(thm)],[949, 1763])).
% 0.75/0.92 tff(1766,plain,
% 0.75/0.92 (c2_1(a144)),
% 0.75/0.92 inference(unit_resolution,[status(thm)],[936, 1763])).
% 0.75/0.92 tff(1767,plain,
% 0.75/0.92 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp16 | c0_1(a144) | c3_1(a144) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c1_1(a128)) | (~c2_1(a144)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp16 | c0_1(a144) | c3_1(a144) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c1_1(a128)) | (~c2_1(a144)))),
% 0.75/0.92 inference(rewrite,[status(thm)],[])).
% 0.75/0.92 tff(1768,plain,
% 0.75/0.92 ((hskp16 | (~ndr1_0) | c3_1(a128) | c2_1(a128) | (~c1_1(a128)) | c3_1(a144) | c0_1(a144) | (~c2_1(a144))) <=> (hskp16 | c0_1(a144) | c3_1(a144) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c1_1(a128)) | (~c2_1(a144)))),
% 0.75/0.92 inference(rewrite,[status(thm)],[])).
% 0.75/0.92 tff(1769,plain,
% 0.75/0.92 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp16 | (~ndr1_0) | c3_1(a128) | c2_1(a128) | (~c1_1(a128)) | c3_1(a144) | c0_1(a144) | (~c2_1(a144)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp16 | c0_1(a144) | c3_1(a144) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c1_1(a128)) | (~c2_1(a144))))),
% 0.75/0.92 inference(monotonicity,[status(thm)],[1768])).
% 0.75/0.92 tff(1770,plain,
% 0.75/0.92 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp16 | (~ndr1_0) | c3_1(a128) | c2_1(a128) | (~c1_1(a128)) | c3_1(a144) | c0_1(a144) | (~c2_1(a144)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp16 | c0_1(a144) | c3_1(a144) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c1_1(a128)) | (~c2_1(a144)))),
% 0.75/0.92 inference(transitivity,[status(thm)],[1769, 1767])).
% 0.75/0.92 tff(1771,plain,
% 0.75/0.92 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | (hskp16 | (~ndr1_0) | c3_1(a128) | c2_1(a128) | (~c1_1(a128)) | c3_1(a144) | c0_1(a144) | (~c2_1(a144)))),
% 0.75/0.92 inference(quant_inst,[status(thm)],[])).
% 0.75/0.92 tff(1772,plain,
% 0.75/0.92 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)))) | hskp16 | c0_1(a144) | c3_1(a144) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c1_1(a128)) | (~c2_1(a144))),
% 0.75/0.92 inference(modus_ponens,[status(thm)],[1771, 1770])).
% 0.75/0.92 tff(1773,plain,
% 0.75/0.92 (hskp16),
% 0.75/0.92 inference(unit_resolution,[status(thm)],[1772, 175, 1766, 1765, 1764, 1494, 1495, 1649, 1629])).
% 0.75/0.92 tff(1774,plain,
% 0.75/0.92 (~c2_1(a151)),
% 0.75/0.92 inference(unit_resolution,[status(thm)],[188, 1773])).
% 0.75/0.92 tff(1775,plain,
% 0.75/0.92 (c1_1(a151)),
% 0.75/0.92 inference(unit_resolution,[status(thm)],[196, 1773])).
% 0.75/0.92 tff(1776,plain,
% 0.75/0.92 (c0_1(a151)),
% 0.75/0.92 inference(unit_resolution,[status(thm)],[231, 1773])).
% 0.75/0.92 tff(1777,plain,
% 0.75/0.92 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp27 | c0_1(a170) | c2_1(a170) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c3_1(a170)))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp27 | c0_1(a170) | c2_1(a170) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c3_1(a170)))),
% 0.75/0.92 inference(rewrite,[status(thm)],[])).
% 0.75/0.92 tff(1778,plain,
% 0.75/0.92 ((hskp27 | (~ndr1_0) | c0_1(a170) | c2_1(a170) | (~c3_1(a170)) | c3_1(a128) | c0_1(a128) | c2_1(a128)) <=> (hskp27 | c0_1(a170) | c2_1(a170) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c3_1(a170)))),
% 0.75/0.92 inference(rewrite,[status(thm)],[])).
% 0.75/0.92 tff(1779,plain,
% 0.75/0.92 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp27 | (~ndr1_0) | c0_1(a170) | c2_1(a170) | (~c3_1(a170)) | c3_1(a128) | c0_1(a128) | c2_1(a128))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp27 | c0_1(a170) | c2_1(a170) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c3_1(a170))))),
% 0.75/0.93 inference(monotonicity,[status(thm)],[1778])).
% 0.75/0.93 tff(1780,plain,
% 0.75/0.93 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp27 | (~ndr1_0) | c0_1(a170) | c2_1(a170) | (~c3_1(a170)) | c3_1(a128) | c0_1(a128) | c2_1(a128))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp27 | c0_1(a170) | c2_1(a170) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c3_1(a170)))),
% 0.75/0.93 inference(transitivity,[status(thm)],[1779, 1777])).
% 0.75/0.93 tff(1781,plain,
% 0.75/0.93 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp27 | (~ndr1_0) | c0_1(a170) | c2_1(a170) | (~c3_1(a170)) | c3_1(a128) | c0_1(a128) | c2_1(a128))),
% 0.75/0.93 inference(quant_inst,[status(thm)],[])).
% 0.75/0.93 tff(1782,plain,
% 0.75/0.93 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp27 | c0_1(a170) | c2_1(a170) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c3_1(a170))),
% 0.75/0.93 inference(modus_ponens,[status(thm)],[1781, 1780])).
% 0.75/0.93 tff(1783,plain,
% 0.75/0.93 (hskp27),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[1782, 175, 1654, 1653, 1652, 1493, 1494, 1495, 1131])).
% 0.75/0.93 tff(1784,plain,
% 0.75/0.93 (c3_1(a137)),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[1146, 1783])).
% 0.75/0.93 tff(1785,plain,
% 0.75/0.93 (c2_1(a137)),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[1154, 1783])).
% 0.75/0.93 tff(1786,plain,
% 0.75/0.93 (c1_1(a137)),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[1162, 1783])).
% 0.75/0.93 tff(1787,plain,
% 0.75/0.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | (c2_1(a151) | c1_1(a139) | c3_1(a139) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | (~c2_1(a139)) | (~c1_1(a151)) | (~c0_1(a151)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | c2_1(a151) | c1_1(a139) | c3_1(a139) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | (~c2_1(a139)) | (~c1_1(a151)) | (~c0_1(a151)))),
% 0.75/0.93 inference(rewrite,[status(thm)],[])).
% 0.75/0.93 tff(1788,plain,
% 0.75/0.93 (((~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | c2_1(a151) | (~c1_1(a151)) | (~c0_1(a151)) | c1_1(a139) | c3_1(a139) | (~c2_1(a139))) <=> (c2_1(a151) | c1_1(a139) | c3_1(a139) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | (~c2_1(a139)) | (~c1_1(a151)) | (~c0_1(a151)))),
% 0.75/0.93 inference(rewrite,[status(thm)],[])).
% 0.75/0.93 tff(1789,plain,
% 0.75/0.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | c2_1(a151) | (~c1_1(a151)) | (~c0_1(a151)) | c1_1(a139) | c3_1(a139) | (~c2_1(a139)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | (c2_1(a151) | c1_1(a139) | c3_1(a139) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | (~c2_1(a139)) | (~c1_1(a151)) | (~c0_1(a151))))),
% 0.75/0.93 inference(monotonicity,[status(thm)],[1788])).
% 0.75/0.93 tff(1790,plain,
% 0.75/0.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | c2_1(a151) | (~c1_1(a151)) | (~c0_1(a151)) | c1_1(a139) | c3_1(a139) | (~c2_1(a139)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | c2_1(a151) | c1_1(a139) | c3_1(a139) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | (~c2_1(a139)) | (~c1_1(a151)) | (~c0_1(a151)))),
% 0.75/0.93 inference(transitivity,[status(thm)],[1789, 1787])).
% 0.75/0.93 tff(1791,plain,
% 0.75/0.93 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | c2_1(a151) | (~c1_1(a151)) | (~c0_1(a151)) | c1_1(a139) | c3_1(a139) | (~c2_1(a139)))),
% 0.75/0.93 inference(quant_inst,[status(thm)],[])).
% 0.75/0.93 tff(1792,plain,
% 0.75/0.93 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | c2_1(a151) | c1_1(a139) | c3_1(a139) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | (~c2_1(a139)) | (~c1_1(a151)) | (~c0_1(a151))),
% 0.75/0.93 inference(modus_ponens,[status(thm)],[1791, 1790])).
% 0.75/0.93 tff(1793,plain,
% 0.75/0.93 (~c2_1(a139)),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[1792, 175, 1786, 1785, 1784, 1776, 1775, 1774, 1639, 1638, 94])).
% 0.75/0.93 tff(1794,plain,
% 0.75/0.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c0_1(a144) | c3_1(a144) | c1_1(a139) | c3_1(a139) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | c2_1(a139) | (~c2_1(a144)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c0_1(a144) | c3_1(a144) | c1_1(a139) | c3_1(a139) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | c2_1(a139) | (~c2_1(a144)))),
% 0.75/0.93 inference(rewrite,[status(thm)],[])).
% 0.75/0.93 tff(1795,plain,
% 0.75/0.93 (((~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | c3_1(a144) | c0_1(a144) | (~c2_1(a144)) | c2_1(a139) | c1_1(a139) | c3_1(a139)) <=> (c0_1(a144) | c3_1(a144) | c1_1(a139) | c3_1(a139) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | c2_1(a139) | (~c2_1(a144)))),
% 0.75/0.93 inference(rewrite,[status(thm)],[])).
% 0.75/0.93 tff(1796,plain,
% 0.75/0.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | c3_1(a144) | c0_1(a144) | (~c2_1(a144)) | c2_1(a139) | c1_1(a139) | c3_1(a139))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c0_1(a144) | c3_1(a144) | c1_1(a139) | c3_1(a139) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | c2_1(a139) | (~c2_1(a144))))),
% 0.75/0.93 inference(monotonicity,[status(thm)],[1795])).
% 0.75/0.93 tff(1797,plain,
% 0.75/0.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | c3_1(a144) | c0_1(a144) | (~c2_1(a144)) | c2_1(a139) | c1_1(a139) | c3_1(a139))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c0_1(a144) | c3_1(a144) | c1_1(a139) | c3_1(a139) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | c2_1(a139) | (~c2_1(a144)))),
% 0.75/0.93 inference(transitivity,[status(thm)],[1796, 1794])).
% 0.75/0.93 tff(1798,plain,
% 0.75/0.93 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | c3_1(a144) | c0_1(a144) | (~c2_1(a144)) | c2_1(a139) | c1_1(a139) | c3_1(a139))),
% 0.75/0.93 inference(quant_inst,[status(thm)],[])).
% 0.75/0.93 tff(1799,plain,
% 0.75/0.93 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c0_1(a144) | c3_1(a144) | c1_1(a139) | c3_1(a139) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | c2_1(a139) | (~c2_1(a144))),
% 0.75/0.93 inference(modus_ponens,[status(thm)],[1798, 1797])).
% 0.75/0.93 tff(1800,plain,
% 0.75/0.93 ($false),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[1799, 175, 1786, 1785, 1784, 1766, 1765, 1764, 1639, 1638, 1104, 1793])).
% 0.75/0.93 tff(1801,plain,(hskp18), inference(lemma,lemma(discharge,[]))).
% 0.75/0.93 tff(1802,plain,
% 0.75/0.93 (((~hskp18) | (~c3_1(a159))) <=> ((~hskp18) | (~c3_1(a159)))),
% 0.75/0.93 inference(rewrite,[status(thm)],[])).
% 0.75/0.93 tff(1803,plain,
% 0.75/0.93 (((~c3_1(a159)) | (~hskp18)) <=> ((~hskp18) | (~c3_1(a159)))),
% 0.75/0.93 inference(rewrite,[status(thm)],[])).
% 0.75/0.93 tff(1804,axiom,((~c3_1(a159)) | (~hskp18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause99')).
% 0.75/0.93 tff(1805,plain,
% 0.75/0.93 ((~hskp18) | (~c3_1(a159))),
% 0.75/0.93 inference(modus_ponens,[status(thm)],[1804, 1803])).
% 0.75/0.93 tff(1806,plain,
% 0.75/0.93 ((~hskp18) | (~c3_1(a159))),
% 0.75/0.93 inference(modus_ponens,[status(thm)],[1805, 1802])).
% 0.75/0.93 tff(1807,plain,
% 0.75/0.93 (~c3_1(a159)),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[1806, 1801])).
% 0.75/0.93 tff(1808,plain,
% 0.75/0.93 (((~hskp18) | (~c2_1(a159))) <=> ((~hskp18) | (~c2_1(a159)))),
% 0.75/0.93 inference(rewrite,[status(thm)],[])).
% 0.75/0.93 tff(1809,plain,
% 0.75/0.93 (((~c2_1(a159)) | (~hskp18)) <=> ((~hskp18) | (~c2_1(a159)))),
% 0.75/0.93 inference(rewrite,[status(thm)],[])).
% 0.75/0.93 tff(1810,axiom,((~c2_1(a159)) | (~hskp18)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause98')).
% 0.75/0.93 tff(1811,plain,
% 0.75/0.93 ((~hskp18) | (~c2_1(a159))),
% 0.75/0.93 inference(modus_ponens,[status(thm)],[1810, 1809])).
% 0.75/0.93 tff(1812,plain,
% 0.75/0.93 ((~hskp18) | (~c2_1(a159))),
% 0.75/0.93 inference(modus_ponens,[status(thm)],[1811, 1808])).
% 0.75/0.93 tff(1813,plain,
% 0.75/0.93 (~c2_1(a159)),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[1812, 1801])).
% 0.75/0.93 tff(1814,plain,
% 0.75/0.93 (((~hskp18) | c0_1(a159)) <=> ((~hskp18) | c0_1(a159))),
% 0.75/0.93 inference(rewrite,[status(thm)],[])).
% 0.75/0.93 tff(1815,axiom,((~hskp18) | c0_1(a159)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause59')).
% 0.75/0.93 tff(1816,plain,
% 0.75/0.93 ((~hskp18) | c0_1(a159)),
% 0.75/0.93 inference(modus_ponens,[status(thm)],[1815, 1814])).
% 0.75/0.93 tff(1817,plain,
% 0.75/0.93 ((~hskp18) | c0_1(a159)),
% 0.75/0.93 inference(modus_ponens,[status(thm)],[1816, 1814])).
% 0.75/0.93 tff(1818,plain,
% 0.75/0.93 ((~hskp18) | c0_1(a159)),
% 0.75/0.93 inference(modus_ponens,[status(thm)],[1817, 1814])).
% 0.75/0.93 tff(1819,plain,
% 0.75/0.93 ((~hskp18) | c0_1(a159)),
% 0.75/0.93 inference(modus_ponens,[status(thm)],[1818, 1814])).
% 0.75/0.93 tff(1820,plain,
% 0.75/0.93 ((~hskp18) | c0_1(a159)),
% 0.75/0.93 inference(modus_ponens,[status(thm)],[1819, 1814])).
% 0.75/0.93 tff(1821,plain,
% 0.75/0.93 (c0_1(a159)),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[1820, 1801])).
% 0.75/0.93 tff(1822,plain,
% 0.75/0.93 (((~![U: $i] : (hskp3 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp3 | hskp1 | c2_1(a159) | c3_1(a159) | (~ndr1_0) | (~c0_1(a159)))) <=> ((~![U: $i] : (hskp3 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | hskp3 | hskp1 | c2_1(a159) | c3_1(a159) | (~ndr1_0) | (~c0_1(a159)))),
% 0.75/0.93 inference(rewrite,[status(thm)],[])).
% 0.75/0.93 tff(1823,plain,
% 0.75/0.93 ((hskp3 | hskp1 | (~ndr1_0) | c3_1(a159) | c2_1(a159) | (~c0_1(a159))) <=> (hskp3 | hskp1 | c2_1(a159) | c3_1(a159) | (~ndr1_0) | (~c0_1(a159)))),
% 0.75/0.93 inference(rewrite,[status(thm)],[])).
% 0.75/0.93 tff(1824,plain,
% 0.75/0.93 (((~![U: $i] : (hskp3 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp3 | hskp1 | (~ndr1_0) | c3_1(a159) | c2_1(a159) | (~c0_1(a159)))) <=> ((~![U: $i] : (hskp3 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp3 | hskp1 | c2_1(a159) | c3_1(a159) | (~ndr1_0) | (~c0_1(a159))))),
% 0.75/0.93 inference(monotonicity,[status(thm)],[1823])).
% 0.75/0.93 tff(1825,plain,
% 0.75/0.93 (((~![U: $i] : (hskp3 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp3 | hskp1 | (~ndr1_0) | c3_1(a159) | c2_1(a159) | (~c0_1(a159)))) <=> ((~![U: $i] : (hskp3 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | hskp3 | hskp1 | c2_1(a159) | c3_1(a159) | (~ndr1_0) | (~c0_1(a159)))),
% 0.75/0.93 inference(transitivity,[status(thm)],[1824, 1822])).
% 0.75/0.93 tff(1826,plain,
% 0.75/0.93 ((~![U: $i] : (hskp3 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | (hskp3 | hskp1 | (~ndr1_0) | c3_1(a159) | c2_1(a159) | (~c0_1(a159)))),
% 0.75/0.93 inference(quant_inst,[status(thm)],[])).
% 0.75/0.93 tff(1827,plain,
% 0.75/0.93 ((~![U: $i] : (hskp3 | hskp1 | (~ndr1_0) | c3_1(U) | c2_1(U) | (~c0_1(U)))) | hskp3 | hskp1 | c2_1(a159) | c3_1(a159) | (~ndr1_0) | (~c0_1(a159))),
% 0.75/0.93 inference(modus_ponens,[status(thm)],[1826, 1825])).
% 0.75/0.93 tff(1828,plain,
% 0.75/0.93 (hskp3 | hskp1),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[1827, 175, 1821, 1813, 1807, 84])).
% 0.75/0.93 tff(1829,plain,
% 0.75/0.93 (hskp1),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[1828, 52])).
% 0.75/0.93 tff(1830,plain,
% 0.75/0.93 (c1_1(a125)),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[572, 1829])).
% 0.75/0.93 tff(1831,plain,
% 0.75/0.93 (c0_1(a125)),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[580, 1829])).
% 0.75/0.93 tff(1832,plain,
% 0.75/0.93 (((~![U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp15 | (~ndr1_0) | c2_1(a125) | (~c0_1(a125)) | (~c1_1(a125)))) <=> ((~![U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp15 | (~ndr1_0) | c2_1(a125) | (~c0_1(a125)) | (~c1_1(a125)))),
% 0.75/0.93 inference(rewrite,[status(thm)],[])).
% 0.75/0.93 tff(1833,plain,
% 0.75/0.93 ((hskp15 | (~ndr1_0) | c2_1(a125) | (~c1_1(a125)) | (~c0_1(a125))) <=> (hskp15 | (~ndr1_0) | c2_1(a125) | (~c0_1(a125)) | (~c1_1(a125)))),
% 0.75/0.93 inference(rewrite,[status(thm)],[])).
% 0.75/0.93 tff(1834,plain,
% 0.75/0.93 (((~![U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp15 | (~ndr1_0) | c2_1(a125) | (~c1_1(a125)) | (~c0_1(a125)))) <=> ((~![U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp15 | (~ndr1_0) | c2_1(a125) | (~c0_1(a125)) | (~c1_1(a125))))),
% 0.75/0.93 inference(monotonicity,[status(thm)],[1833])).
% 0.75/0.93 tff(1835,plain,
% 0.75/0.93 (((~![U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp15 | (~ndr1_0) | c2_1(a125) | (~c1_1(a125)) | (~c0_1(a125)))) <=> ((~![U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp15 | (~ndr1_0) | c2_1(a125) | (~c0_1(a125)) | (~c1_1(a125)))),
% 0.75/0.93 inference(transitivity,[status(thm)],[1834, 1832])).
% 0.75/0.93 tff(1836,plain,
% 0.75/0.93 ((~![U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp15 | (~ndr1_0) | c2_1(a125) | (~c1_1(a125)) | (~c0_1(a125)))),
% 0.75/0.93 inference(quant_inst,[status(thm)],[])).
% 0.75/0.93 tff(1837,plain,
% 0.75/0.93 ((~![U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp15 | (~ndr1_0) | c2_1(a125) | (~c0_1(a125)) | (~c1_1(a125))),
% 0.75/0.93 inference(modus_ponens,[status(thm)],[1836, 1835])).
% 0.75/0.93 tff(1838,plain,
% 0.75/0.93 (hskp15 | c2_1(a125)),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[1837, 175, 1831, 1830, 63])).
% 0.75/0.93 tff(1839,plain,
% 0.75/0.93 (c2_1(a125)),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[1838, 74])).
% 0.75/0.93 tff(1840,plain,
% 0.75/0.93 (~c3_1(a125)),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[564, 1829])).
% 0.75/0.93 tff(1841,plain,
% 0.75/0.93 (hskp13),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[1117, 175, 1831, 1830, 1840, 21, 1839])).
% 0.75/0.93 tff(1842,plain,
% 0.75/0.93 (~c3_1(a144)),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[928, 1841])).
% 0.75/0.93 tff(1843,plain,
% 0.75/0.93 (~c0_1(a144)),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[949, 1841])).
% 0.75/0.93 tff(1844,plain,
% 0.75/0.93 (c2_1(a144)),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[936, 1841])).
% 0.75/0.93 tff(1845,plain,
% 0.75/0.93 (hskp29),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[1248, 175, 52, 1844, 1843, 1842, 73])).
% 0.75/0.93 tff(1846,plain,
% 0.75/0.93 (c1_1(a150)),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[1264, 1845])).
% 0.75/0.93 tff(1847,plain,
% 0.75/0.93 (c0_1(a150)),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[1272, 1845])).
% 0.75/0.93 tff(1848,plain,
% 0.75/0.93 (((~![U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp15 | (~ndr1_0) | c2_1(a150) | (~c0_1(a150)) | (~c1_1(a150)))) <=> ((~![U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp15 | (~ndr1_0) | c2_1(a150) | (~c0_1(a150)) | (~c1_1(a150)))),
% 0.75/0.93 inference(rewrite,[status(thm)],[])).
% 0.75/0.93 tff(1849,plain,
% 0.75/0.93 ((hskp15 | (~ndr1_0) | c2_1(a150) | (~c1_1(a150)) | (~c0_1(a150))) <=> (hskp15 | (~ndr1_0) | c2_1(a150) | (~c0_1(a150)) | (~c1_1(a150)))),
% 0.75/0.93 inference(rewrite,[status(thm)],[])).
% 0.75/0.93 tff(1850,plain,
% 0.75/0.93 (((~![U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp15 | (~ndr1_0) | c2_1(a150) | (~c1_1(a150)) | (~c0_1(a150)))) <=> ((~![U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp15 | (~ndr1_0) | c2_1(a150) | (~c0_1(a150)) | (~c1_1(a150))))),
% 0.75/0.93 inference(monotonicity,[status(thm)],[1849])).
% 0.75/0.93 tff(1851,plain,
% 0.75/0.93 (((~![U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp15 | (~ndr1_0) | c2_1(a150) | (~c1_1(a150)) | (~c0_1(a150)))) <=> ((~![U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp15 | (~ndr1_0) | c2_1(a150) | (~c0_1(a150)) | (~c1_1(a150)))),
% 0.75/0.93 inference(transitivity,[status(thm)],[1850, 1848])).
% 0.75/0.93 tff(1852,plain,
% 0.75/0.93 ((~![U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp15 | (~ndr1_0) | c2_1(a150) | (~c1_1(a150)) | (~c0_1(a150)))),
% 0.75/0.93 inference(quant_inst,[status(thm)],[])).
% 0.75/0.93 tff(1853,plain,
% 0.75/0.93 ((~![U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp15 | (~ndr1_0) | c2_1(a150) | (~c0_1(a150)) | (~c1_1(a150))),
% 0.75/0.93 inference(modus_ponens,[status(thm)],[1852, 1851])).
% 0.75/0.93 tff(1854,plain,
% 0.75/0.93 (c2_1(a150)),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[1853, 175, 74, 1847, 1846, 63])).
% 0.75/0.93 tff(1855,plain,
% 0.75/0.93 (((~![U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp15 | c2_1(a159) | (~ndr1_0) | (~c1_1(a159)) | (~c0_1(a159)))) <=> ((~![U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp15 | c2_1(a159) | (~ndr1_0) | (~c1_1(a159)) | (~c0_1(a159)))),
% 0.75/0.93 inference(rewrite,[status(thm)],[])).
% 0.75/0.93 tff(1856,plain,
% 0.75/0.93 ((hskp15 | (~ndr1_0) | c2_1(a159) | (~c1_1(a159)) | (~c0_1(a159))) <=> (hskp15 | c2_1(a159) | (~ndr1_0) | (~c1_1(a159)) | (~c0_1(a159)))),
% 0.75/0.93 inference(rewrite,[status(thm)],[])).
% 0.75/0.93 tff(1857,plain,
% 0.75/0.93 (((~![U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp15 | (~ndr1_0) | c2_1(a159) | (~c1_1(a159)) | (~c0_1(a159)))) <=> ((~![U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp15 | c2_1(a159) | (~ndr1_0) | (~c1_1(a159)) | (~c0_1(a159))))),
% 0.75/0.93 inference(monotonicity,[status(thm)],[1856])).
% 0.75/0.93 tff(1858,plain,
% 0.75/0.93 (((~![U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp15 | (~ndr1_0) | c2_1(a159) | (~c1_1(a159)) | (~c0_1(a159)))) <=> ((~![U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp15 | c2_1(a159) | (~ndr1_0) | (~c1_1(a159)) | (~c0_1(a159)))),
% 0.75/0.93 inference(transitivity,[status(thm)],[1857, 1855])).
% 0.75/0.93 tff(1859,plain,
% 0.75/0.93 ((~![U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp15 | (~ndr1_0) | c2_1(a159) | (~c1_1(a159)) | (~c0_1(a159)))),
% 0.75/0.93 inference(quant_inst,[status(thm)],[])).
% 0.75/0.93 tff(1860,plain,
% 0.75/0.93 ((~![U: $i] : (hskp15 | (~ndr1_0) | c2_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp15 | c2_1(a159) | (~ndr1_0) | (~c1_1(a159)) | (~c0_1(a159))),
% 0.75/0.93 inference(modus_ponens,[status(thm)],[1859, 1858])).
% 0.75/0.93 tff(1861,plain,
% 0.75/0.93 (hskp15 | (~c1_1(a159))),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[1860, 175, 1821, 1813, 63])).
% 0.75/0.93 tff(1862,plain,
% 0.75/0.93 (~c1_1(a159)),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[1861, 74])).
% 0.75/0.93 tff(1863,plain,
% 0.75/0.93 (c3_1(a150)),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[1256, 1845])).
% 0.75/0.93 tff(1864,plain,
% 0.75/0.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c2_1(a159) | c3_1(a159) | c0_1(a144) | c3_1(a144) | (~ndr1_0) | (~c3_1(a150)) | (~c2_1(a150)) | (~c1_1(a150)) | (~c2_1(a144)) | c1_1(a159))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c2_1(a159) | c3_1(a159) | c0_1(a144) | c3_1(a144) | (~ndr1_0) | (~c3_1(a150)) | (~c2_1(a150)) | (~c1_1(a150)) | (~c2_1(a144)) | c1_1(a159))),
% 0.75/0.93 inference(rewrite,[status(thm)],[])).
% 0.75/0.93 tff(1865,plain,
% 0.75/0.93 (((~ndr1_0) | (~c2_1(a150)) | (~c3_1(a150)) | (~c1_1(a150)) | c3_1(a144) | c0_1(a144) | (~c2_1(a144)) | c2_1(a159) | c1_1(a159) | c3_1(a159)) <=> (c2_1(a159) | c3_1(a159) | c0_1(a144) | c3_1(a144) | (~ndr1_0) | (~c3_1(a150)) | (~c2_1(a150)) | (~c1_1(a150)) | (~c2_1(a144)) | c1_1(a159))),
% 0.75/0.93 inference(rewrite,[status(thm)],[])).
% 0.75/0.93 tff(1866,plain,
% 0.75/0.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | (~c2_1(a150)) | (~c3_1(a150)) | (~c1_1(a150)) | c3_1(a144) | c0_1(a144) | (~c2_1(a144)) | c2_1(a159) | c1_1(a159) | c3_1(a159))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c2_1(a159) | c3_1(a159) | c0_1(a144) | c3_1(a144) | (~ndr1_0) | (~c3_1(a150)) | (~c2_1(a150)) | (~c1_1(a150)) | (~c2_1(a144)) | c1_1(a159)))),
% 0.75/0.93 inference(monotonicity,[status(thm)],[1865])).
% 0.75/0.93 tff(1867,plain,
% 0.75/0.93 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | (~c2_1(a150)) | (~c3_1(a150)) | (~c1_1(a150)) | c3_1(a144) | c0_1(a144) | (~c2_1(a144)) | c2_1(a159) | c1_1(a159) | c3_1(a159))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c2_1(a159) | c3_1(a159) | c0_1(a144) | c3_1(a144) | (~ndr1_0) | (~c3_1(a150)) | (~c2_1(a150)) | (~c1_1(a150)) | (~c2_1(a144)) | c1_1(a159))),
% 0.75/0.93 inference(transitivity,[status(thm)],[1866, 1864])).
% 0.75/0.93 tff(1868,plain,
% 0.75/0.93 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | (~c2_1(a150)) | (~c3_1(a150)) | (~c1_1(a150)) | c3_1(a144) | c0_1(a144) | (~c2_1(a144)) | c2_1(a159) | c1_1(a159) | c3_1(a159))),
% 0.75/0.93 inference(quant_inst,[status(thm)],[])).
% 0.75/0.93 tff(1869,plain,
% 0.75/0.93 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c2_1(a159) | c3_1(a159) | c0_1(a144) | c3_1(a144) | (~ndr1_0) | (~c3_1(a150)) | (~c2_1(a150)) | (~c1_1(a150)) | (~c2_1(a144)) | c1_1(a159)),
% 0.75/0.93 inference(modus_ponens,[status(thm)],[1868, 1867])).
% 0.75/0.93 tff(1870,plain,
% 0.75/0.93 ($false),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[1869, 175, 1846, 1863, 1844, 1813, 1807, 1843, 1842, 1104, 1862, 1854])).
% 0.75/0.93 tff(1871,plain,(hskp15 | hskp3), inference(lemma,lemma(discharge,[]))).
% 0.75/0.93 tff(1872,plain,
% 0.75/0.93 (hskp15),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[1871, 52])).
% 0.75/0.93 tff(1873,plain,
% 0.75/0.93 (c3_1(a149)),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[246, 1872])).
% 0.75/0.93 tff(1874,plain,
% 0.75/0.93 (~c2_1(a149)),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[525, 1872])).
% 0.75/0.93 tff(1875,plain,
% 0.75/0.93 (hskp14 | c0_1(a149)),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[718, 175, 52, 1873, 1874, 51])).
% 0.75/0.93 tff(1876,plain,
% 0.75/0.93 (c0_1(a149)),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[1875, 724])).
% 0.75/0.93 tff(1877,plain,
% 0.75/0.93 (~c1_1(a149)),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[531, 1872])).
% 0.75/0.93 tff(1878,plain,
% 0.75/0.93 (~hskp6),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[741, 724, 52, 1877, 1876, 1873])).
% 0.75/0.93 tff(1879,plain,
% 0.75/0.93 (hskp12),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[587, 175, 1831, 1830, 1840, 224])).
% 0.75/0.93 tff(1880,plain,
% 0.75/0.93 (~c0_1(a140)),
% 0.75/0.93 inference(unit_resolution,[status(thm)],[593, 1879])).
% 0.75/0.93 tff(1881,plain,
% 0.75/0.93 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp17 | c2_1(a159) | c3_1(a159) | c2_1(a149) | (~ndr1_0) | (~c3_1(a149)) | (~c0_1(a149)) | (~c0_1(a159)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp17 | c2_1(a159) | c3_1(a159) | c2_1(a149) | (~ndr1_0) | (~c3_1(a149)) | (~c0_1(a149)) | (~c0_1(a159)))),
% 0.79/0.93 inference(rewrite,[status(thm)],[])).
% 0.79/0.93 tff(1882,plain,
% 0.79/0.93 ((hskp17 | (~ndr1_0) | c2_1(a149) | (~c3_1(a149)) | (~c0_1(a149)) | c3_1(a159) | c2_1(a159) | (~c0_1(a159))) <=> (hskp17 | c2_1(a159) | c3_1(a159) | c2_1(a149) | (~ndr1_0) | (~c3_1(a149)) | (~c0_1(a149)) | (~c0_1(a159)))),
% 0.79/0.93 inference(rewrite,[status(thm)],[])).
% 0.79/0.93 tff(1883,plain,
% 0.79/0.93 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a149) | (~c3_1(a149)) | (~c0_1(a149)) | c3_1(a159) | c2_1(a159) | (~c0_1(a159)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp17 | c2_1(a159) | c3_1(a159) | c2_1(a149) | (~ndr1_0) | (~c3_1(a149)) | (~c0_1(a149)) | (~c0_1(a159))))),
% 0.79/0.93 inference(monotonicity,[status(thm)],[1882])).
% 0.79/0.93 tff(1884,plain,
% 0.79/0.93 (((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a149) | (~c3_1(a149)) | (~c0_1(a149)) | c3_1(a159) | c2_1(a159) | (~c0_1(a159)))) <=> ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp17 | c2_1(a159) | c3_1(a159) | c2_1(a149) | (~ndr1_0) | (~c3_1(a149)) | (~c0_1(a149)) | (~c0_1(a159)))),
% 0.79/0.93 inference(transitivity,[status(thm)],[1883, 1881])).
% 0.79/0.93 tff(1885,plain,
% 0.79/0.93 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp17 | (~ndr1_0) | c2_1(a149) | (~c3_1(a149)) | (~c0_1(a149)) | c3_1(a159) | c2_1(a159) | (~c0_1(a159)))),
% 0.79/0.93 inference(quant_inst,[status(thm)],[])).
% 0.79/0.93 tff(1886,plain,
% 0.79/0.93 ((~![V: $i, U: $i] : (hskp17 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c2_1(V) | (~c0_1(V)))) | hskp17 | c2_1(a159) | c3_1(a159) | c2_1(a149) | (~ndr1_0) | (~c3_1(a149)) | (~c0_1(a149)) | (~c0_1(a159))),
% 0.79/0.93 inference(modus_ponens,[status(thm)],[1885, 1884])).
% 0.79/0.93 tff(1887,plain,
% 0.79/0.93 (hskp17 | (~c0_1(a149))),
% 0.79/0.93 inference(unit_resolution,[status(thm)],[1886, 175, 1821, 1873, 1813, 1807, 1874, 269])).
% 0.79/0.93 tff(1888,plain,
% 0.79/0.93 (hskp17),
% 0.79/0.93 inference(unit_resolution,[status(thm)],[1887, 1876])).
% 0.79/0.93 tff(1889,plain,
% 0.79/0.93 (~c3_1(a158)),
% 0.79/0.93 inference(unit_resolution,[status(thm)],[411, 1888])).
% 0.79/0.93 tff(1890,plain,
% 0.79/0.93 (c3_1(a140)),
% 0.79/0.93 inference(unit_resolution,[status(thm)],[604, 1879])).
% 0.79/0.93 tff(1891,plain,
% 0.79/0.93 (c1_1(a140)),
% 0.79/0.93 inference(unit_resolution,[status(thm)],[801, 1879])).
% 0.79/0.93 tff(1892,plain,
% 0.79/0.93 (c1_1(a158)),
% 0.79/0.93 inference(unit_resolution,[status(thm)],[425, 1888])).
% 0.79/0.93 tff(1893,plain,
% 0.79/0.93 (~hskp6),
% 0.79/0.93 inference(unit_resolution,[status(thm)],[741, 1876, 52, 1877, 724, 1873])).
% 0.79/0.93 tff(1894,plain,
% 0.79/0.93 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | c3_1(a158) | c0_1(a140) | (~ndr1_0) | (~c3_1(a140)) | (~c1_1(a140)) | (~c1_1(a158)) | c0_1(a158))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp6 | c3_1(a158) | c0_1(a140) | (~ndr1_0) | (~c3_1(a140)) | (~c1_1(a140)) | (~c1_1(a158)) | c0_1(a158))),
% 0.79/0.93 inference(rewrite,[status(thm)],[])).
% 0.79/0.93 tff(1895,plain,
% 0.79/0.93 ((hskp6 | (~ndr1_0) | c0_1(a140) | (~c3_1(a140)) | (~c1_1(a140)) | c3_1(a158) | c0_1(a158) | (~c1_1(a158))) <=> (hskp6 | c3_1(a158) | c0_1(a140) | (~ndr1_0) | (~c3_1(a140)) | (~c1_1(a140)) | (~c1_1(a158)) | c0_1(a158))),
% 0.79/0.93 inference(rewrite,[status(thm)],[])).
% 0.79/0.93 tff(1896,plain,
% 0.79/0.93 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | (~ndr1_0) | c0_1(a140) | (~c3_1(a140)) | (~c1_1(a140)) | c3_1(a158) | c0_1(a158) | (~c1_1(a158)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | c3_1(a158) | c0_1(a140) | (~ndr1_0) | (~c3_1(a140)) | (~c1_1(a140)) | (~c1_1(a158)) | c0_1(a158)))),
% 0.79/0.93 inference(monotonicity,[status(thm)],[1895])).
% 0.79/0.93 tff(1897,plain,
% 0.79/0.93 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | (~ndr1_0) | c0_1(a140) | (~c3_1(a140)) | (~c1_1(a140)) | c3_1(a158) | c0_1(a158) | (~c1_1(a158)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp6 | c3_1(a158) | c0_1(a140) | (~ndr1_0) | (~c3_1(a140)) | (~c1_1(a140)) | (~c1_1(a158)) | c0_1(a158))),
% 0.79/0.93 inference(transitivity,[status(thm)],[1896, 1894])).
% 0.79/0.93 tff(1898,plain,
% 0.79/0.93 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | (~ndr1_0) | c0_1(a140) | (~c3_1(a140)) | (~c1_1(a140)) | c3_1(a158) | c0_1(a158) | (~c1_1(a158)))),
% 0.79/0.93 inference(quant_inst,[status(thm)],[])).
% 0.79/0.93 tff(1899,plain,
% 0.79/0.93 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp6 | c3_1(a158) | c0_1(a140) | (~ndr1_0) | (~c3_1(a140)) | (~c1_1(a140)) | (~c1_1(a158)) | c0_1(a158)),
% 0.79/0.94 inference(modus_ponens,[status(thm)],[1898, 1897])).
% 0.79/0.94 tff(1900,plain,
% 0.79/0.94 (c0_1(a158)),
% 0.79/0.94 inference(unit_resolution,[status(thm)],[1899, 175, 1893, 1892, 1891, 1890, 1889, 1880, 315])).
% 0.79/0.94 tff(1901,plain,
% 0.79/0.94 (hskp14 | c2_1(a140)),
% 0.79/0.94 inference(unit_resolution,[status(thm)],[829, 175, 52, 1890, 1880, 51])).
% 0.79/0.94 tff(1902,plain,
% 0.79/0.94 (c2_1(a140)),
% 0.79/0.94 inference(unit_resolution,[status(thm)],[1901, 724])).
% 0.79/0.94 tff(1903,plain,
% 0.79/0.94 (hskp9),
% 0.79/0.94 inference(unit_resolution,[status(thm)],[753, 1893, 53])).
% 0.79/0.94 tff(1904,plain,
% 0.79/0.94 (~c3_1(a136)),
% 0.79/0.94 inference(unit_resolution,[status(thm)],[759, 1903])).
% 0.79/0.94 tff(1905,plain,
% 0.79/0.94 (c2_1(a136)),
% 0.79/0.94 inference(unit_resolution,[status(thm)],[767, 1903])).
% 0.79/0.94 tff(1906,plain,
% 0.79/0.94 (c0_1(a136)),
% 0.79/0.94 inference(unit_resolution,[status(thm)],[783, 1903])).
% 0.79/0.94 tff(1907,plain,
% 0.79/0.94 (~c1_1(a136)),
% 0.79/0.94 inference(unit_resolution,[status(thm)],[1337, 175, 11, 1906, 1905, 1904, 21])).
% 0.79/0.94 tff(1908,plain,
% 0.79/0.94 (~c2_1(a158)),
% 0.79/0.94 inference(unit_resolution,[status(thm)],[417, 1888])).
% 0.79/0.94 tff(1909,plain,
% 0.79/0.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | (c2_1(a158) | c3_1(a136) | (~ndr1_0) | c1_1(a136) | (~c2_1(a136)) | (~c2_1(a140)) | (~c3_1(a140)) | (~c1_1(a140)) | (~c1_1(a158)) | (~c0_1(a158)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | c2_1(a158) | c3_1(a136) | (~ndr1_0) | c1_1(a136) | (~c2_1(a136)) | (~c2_1(a140)) | (~c3_1(a140)) | (~c1_1(a140)) | (~c1_1(a158)) | (~c0_1(a158)))),
% 0.79/0.94 inference(rewrite,[status(thm)],[])).
% 0.79/0.94 tff(1910,plain,
% 0.79/0.94 (((~ndr1_0) | (~c2_1(a140)) | (~c3_1(a140)) | (~c1_1(a140)) | c2_1(a158) | (~c1_1(a158)) | (~c0_1(a158)) | c1_1(a136) | c3_1(a136) | (~c2_1(a136))) <=> (c2_1(a158) | c3_1(a136) | (~ndr1_0) | c1_1(a136) | (~c2_1(a136)) | (~c2_1(a140)) | (~c3_1(a140)) | (~c1_1(a140)) | (~c1_1(a158)) | (~c0_1(a158)))),
% 0.79/0.94 inference(rewrite,[status(thm)],[])).
% 0.79/0.94 tff(1911,plain,
% 0.79/0.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a140)) | (~c3_1(a140)) | (~c1_1(a140)) | c2_1(a158) | (~c1_1(a158)) | (~c0_1(a158)) | c1_1(a136) | c3_1(a136) | (~c2_1(a136)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | (c2_1(a158) | c3_1(a136) | (~ndr1_0) | c1_1(a136) | (~c2_1(a136)) | (~c2_1(a140)) | (~c3_1(a140)) | (~c1_1(a140)) | (~c1_1(a158)) | (~c0_1(a158))))),
% 0.79/0.94 inference(monotonicity,[status(thm)],[1910])).
% 0.79/0.94 tff(1912,plain,
% 0.79/0.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a140)) | (~c3_1(a140)) | (~c1_1(a140)) | c2_1(a158) | (~c1_1(a158)) | (~c0_1(a158)) | c1_1(a136) | c3_1(a136) | (~c2_1(a136)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | c2_1(a158) | c3_1(a136) | (~ndr1_0) | c1_1(a136) | (~c2_1(a136)) | (~c2_1(a140)) | (~c3_1(a140)) | (~c1_1(a140)) | (~c1_1(a158)) | (~c0_1(a158)))),
% 0.79/0.94 inference(transitivity,[status(thm)],[1911, 1909])).
% 0.79/0.94 tff(1913,plain,
% 0.79/0.94 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a140)) | (~c3_1(a140)) | (~c1_1(a140)) | c2_1(a158) | (~c1_1(a158)) | (~c0_1(a158)) | c1_1(a136) | c3_1(a136) | (~c2_1(a136)))),
% 0.79/0.94 inference(quant_inst,[status(thm)],[])).
% 0.79/0.94 tff(1914,plain,
% 0.79/0.94 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | c2_1(a158) | c3_1(a136) | (~ndr1_0) | c1_1(a136) | (~c2_1(a136)) | (~c2_1(a140)) | (~c3_1(a140)) | (~c1_1(a140)) | (~c1_1(a158)) | (~c0_1(a158))),
% 0.79/0.94 inference(modus_ponens,[status(thm)],[1913, 1912])).
% 0.79/0.94 tff(1915,plain,
% 0.79/0.94 ($false),
% 0.79/0.94 inference(unit_resolution,[status(thm)],[1914, 175, 1892, 1891, 1890, 1905, 1908, 1904, 94, 1907, 1902, 1900])).
% 0.79/0.94 tff(1916,plain,(hskp14 | hskp13 | hskp21 | hskp3), inference(lemma,lemma(discharge,[]))).
% 0.79/0.94 tff(1917,plain,
% 0.79/0.94 (hskp14),
% 0.79/0.94 inference(unit_resolution,[status(thm)],[1916, 11, 53, 52])).
% 0.79/0.94 tff(1918,plain,
% 0.79/0.94 (~c1_1(a145)),
% 0.79/0.94 inference(unit_resolution,[status(thm)],[495, 1917])).
% 0.79/0.94 tff(1919,plain,
% 0.79/0.94 (~c3_1(a145)),
% 0.79/0.94 inference(unit_resolution,[status(thm)],[489, 1917])).
% 0.79/0.94 tff(1920,plain,
% 0.79/0.94 (~c0_1(a145)),
% 0.79/0.94 inference(unit_resolution,[status(thm)],[508, 1917])).
% 0.79/0.94 tff(1921,plain,
% 0.79/0.94 (c0_1(a149)),
% 0.79/0.94 inference(unit_resolution,[status(thm)],[1354, 1920, 1919, 52, 1873, 1874, 1918])).
% 0.79/0.94 tff(1922,plain,
% 0.79/0.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a149) | c2_1(a149) | c0_1(a145) | c1_1(a145) | c3_1(a145) | c0_1(a133) | c1_1(a133) | c2_1(a133) | (~ndr1_0) | (~c0_1(a149)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a149) | c2_1(a149) | c0_1(a145) | c1_1(a145) | c3_1(a145) | c0_1(a133) | c1_1(a133) | c2_1(a133) | (~ndr1_0) | (~c0_1(a149)))),
% 0.79/0.94 inference(rewrite,[status(thm)],[])).
% 0.79/0.94 tff(1923,plain,
% 0.79/0.94 (((~ndr1_0) | c1_1(a149) | c2_1(a149) | (~c0_1(a149)) | c3_1(a145) | c1_1(a145) | c0_1(a145) | c2_1(a133) | c1_1(a133) | c0_1(a133)) <=> (c1_1(a149) | c2_1(a149) | c0_1(a145) | c1_1(a145) | c3_1(a145) | c0_1(a133) | c1_1(a133) | c2_1(a133) | (~ndr1_0) | (~c0_1(a149)))),
% 0.79/0.94 inference(rewrite,[status(thm)],[])).
% 0.79/0.94 tff(1924,plain,
% 0.79/0.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a149) | c2_1(a149) | (~c0_1(a149)) | c3_1(a145) | c1_1(a145) | c0_1(a145) | c2_1(a133) | c1_1(a133) | c0_1(a133))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a149) | c2_1(a149) | c0_1(a145) | c1_1(a145) | c3_1(a145) | c0_1(a133) | c1_1(a133) | c2_1(a133) | (~ndr1_0) | (~c0_1(a149))))),
% 0.79/0.94 inference(monotonicity,[status(thm)],[1923])).
% 0.79/0.94 tff(1925,plain,
% 0.79/0.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a149) | c2_1(a149) | (~c0_1(a149)) | c3_1(a145) | c1_1(a145) | c0_1(a145) | c2_1(a133) | c1_1(a133) | c0_1(a133))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a149) | c2_1(a149) | c0_1(a145) | c1_1(a145) | c3_1(a145) | c0_1(a133) | c1_1(a133) | c2_1(a133) | (~ndr1_0) | (~c0_1(a149)))),
% 0.79/0.94 inference(transitivity,[status(thm)],[1924, 1922])).
% 0.79/0.94 tff(1926,plain,
% 0.79/0.94 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a149) | c2_1(a149) | (~c0_1(a149)) | c3_1(a145) | c1_1(a145) | c0_1(a145) | c2_1(a133) | c1_1(a133) | c0_1(a133))),
% 0.79/0.94 inference(quant_inst,[status(thm)],[])).
% 0.79/0.94 tff(1927,plain,
% 0.79/0.94 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a149) | c2_1(a149) | c0_1(a145) | c1_1(a145) | c3_1(a145) | c0_1(a133) | c1_1(a133) | c2_1(a133) | (~ndr1_0) | (~c0_1(a149))),
% 0.79/0.94 inference(modus_ponens,[status(thm)],[1926, 1925])).
% 0.79/0.94 tff(1928,plain,
% 0.79/0.94 ($false),
% 0.79/0.94 inference(unit_resolution,[status(thm)],[1927, 175, 596, 595, 1314, 1306, 1305, 723, 733, 722, 460, 732])).
% 0.79/0.94 tff(1929,plain,((~hskp6) | c1_1(a149) | c2_1(a149) | c0_1(a145) | c1_1(a145) | c3_1(a145) | (~c0_1(a149))), inference(lemma,lemma(discharge,[]))).
% 0.79/0.94 tff(1930,plain,
% 0.79/0.94 (~hskp6),
% 0.79/0.94 inference(unit_resolution,[status(thm)],[1929, 1920, 1874, 1877, 1918, 1919, 1921])).
% 0.79/0.94 tff(1931,plain,
% 0.79/0.94 (hskp17),
% 0.79/0.94 inference(unit_resolution,[status(thm)],[1887, 1921])).
% 0.79/0.94 tff(1932,plain,
% 0.79/0.94 (~c3_1(a158)),
% 0.79/0.94 inference(unit_resolution,[status(thm)],[411, 1931])).
% 0.79/0.94 tff(1933,plain,
% 0.79/0.94 (c1_1(a158)),
% 0.79/0.94 inference(unit_resolution,[status(thm)],[425, 1931])).
% 0.79/0.94 tff(1934,plain,
% 0.79/0.94 (hskp6 | c0_1(a158)),
% 0.79/0.94 inference(unit_resolution,[status(thm)],[1899, 175, 1933, 1891, 1890, 1932, 1880, 315])).
% 0.79/0.94 tff(1935,plain,
% 0.79/0.94 (c0_1(a158)),
% 0.79/0.94 inference(unit_resolution,[status(thm)],[1934, 1930])).
% 0.79/0.94 tff(1936,plain,
% 0.79/0.94 (hskp9),
% 0.79/0.94 inference(unit_resolution,[status(thm)],[753, 1930, 53])).
% 0.79/0.94 tff(1937,plain,
% 0.79/0.94 (c2_1(a136)),
% 0.79/0.94 inference(unit_resolution,[status(thm)],[767, 1936])).
% 0.79/0.94 tff(1938,plain,
% 0.79/0.94 (c0_1(a136)),
% 0.79/0.94 inference(unit_resolution,[status(thm)],[783, 1936])).
% 0.79/0.94 tff(1939,plain,
% 0.79/0.94 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp13 | c3_1(a158) | (~ndr1_0) | (~c1_1(a136)) | (~c0_1(a136)) | (~c2_1(a136)) | (~c1_1(a158)) | (~c0_1(a158)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp13 | c3_1(a158) | (~ndr1_0) | (~c1_1(a136)) | (~c0_1(a136)) | (~c2_1(a136)) | (~c1_1(a158)) | (~c0_1(a158)))),
% 0.79/0.94 inference(rewrite,[status(thm)],[])).
% 0.79/0.94 tff(1940,plain,
% 0.79/0.94 ((hskp13 | (~ndr1_0) | (~c2_1(a136)) | (~c1_1(a136)) | (~c0_1(a136)) | c3_1(a158) | (~c1_1(a158)) | (~c0_1(a158))) <=> (hskp13 | c3_1(a158) | (~ndr1_0) | (~c1_1(a136)) | (~c0_1(a136)) | (~c2_1(a136)) | (~c1_1(a158)) | (~c0_1(a158)))),
% 0.79/0.94 inference(rewrite,[status(thm)],[])).
% 0.79/0.94 tff(1941,plain,
% 0.79/0.94 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp13 | (~ndr1_0) | (~c2_1(a136)) | (~c1_1(a136)) | (~c0_1(a136)) | c3_1(a158) | (~c1_1(a158)) | (~c0_1(a158)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp13 | c3_1(a158) | (~ndr1_0) | (~c1_1(a136)) | (~c0_1(a136)) | (~c2_1(a136)) | (~c1_1(a158)) | (~c0_1(a158))))),
% 0.79/0.94 inference(monotonicity,[status(thm)],[1940])).
% 0.79/0.94 tff(1942,plain,
% 0.79/0.94 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp13 | (~ndr1_0) | (~c2_1(a136)) | (~c1_1(a136)) | (~c0_1(a136)) | c3_1(a158) | (~c1_1(a158)) | (~c0_1(a158)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp13 | c3_1(a158) | (~ndr1_0) | (~c1_1(a136)) | (~c0_1(a136)) | (~c2_1(a136)) | (~c1_1(a158)) | (~c0_1(a158)))),
% 0.79/0.94 inference(transitivity,[status(thm)],[1941, 1939])).
% 0.79/0.94 tff(1943,plain,
% 0.79/0.94 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp13 | (~ndr1_0) | (~c2_1(a136)) | (~c1_1(a136)) | (~c0_1(a136)) | c3_1(a158) | (~c1_1(a158)) | (~c0_1(a158)))),
% 0.79/0.94 inference(quant_inst,[status(thm)],[])).
% 0.79/0.94 tff(1944,plain,
% 0.79/0.94 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp13 | c3_1(a158) | (~ndr1_0) | (~c1_1(a136)) | (~c0_1(a136)) | (~c2_1(a136)) | (~c1_1(a158)) | (~c0_1(a158))),
% 0.79/0.94 inference(modus_ponens,[status(thm)],[1943, 1942])).
% 0.79/0.94 tff(1945,plain,
% 0.79/0.94 (~c1_1(a136)),
% 0.79/0.94 inference(unit_resolution,[status(thm)],[1944, 175, 11, 1933, 1938, 1937, 1932, 21, 1935])).
% 0.79/0.94 tff(1946,plain,
% 0.79/0.94 (~c3_1(a136)),
% 0.79/0.94 inference(unit_resolution,[status(thm)],[759, 1936])).
% 0.79/0.94 tff(1947,plain,
% 0.79/0.94 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp3 | c0_1(a140) | c3_1(a136) | (~ndr1_0) | c1_1(a136) | (~c2_1(a136)) | c2_1(a140) | (~c3_1(a140)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp3 | c0_1(a140) | c3_1(a136) | (~ndr1_0) | c1_1(a136) | (~c2_1(a136)) | c2_1(a140) | (~c3_1(a140)))),
% 0.79/0.94 inference(rewrite,[status(thm)],[])).
% 0.79/0.94 tff(1948,plain,
% 0.79/0.94 ((hskp3 | (~ndr1_0) | c3_1(a136) | c1_1(a136) | (~c2_1(a136)) | c0_1(a140) | c2_1(a140) | (~c3_1(a140))) <=> (hskp3 | c0_1(a140) | c3_1(a136) | (~ndr1_0) | c1_1(a136) | (~c2_1(a136)) | c2_1(a140) | (~c3_1(a140)))),
% 0.79/0.94 inference(rewrite,[status(thm)],[])).
% 0.79/0.94 tff(1949,plain,
% 0.79/0.94 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp3 | (~ndr1_0) | c3_1(a136) | c1_1(a136) | (~c2_1(a136)) | c0_1(a140) | c2_1(a140) | (~c3_1(a140)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp3 | c0_1(a140) | c3_1(a136) | (~ndr1_0) | c1_1(a136) | (~c2_1(a136)) | c2_1(a140) | (~c3_1(a140))))),
% 0.79/0.94 inference(monotonicity,[status(thm)],[1948])).
% 0.79/0.94 tff(1950,plain,
% 0.79/0.94 (((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp3 | (~ndr1_0) | c3_1(a136) | c1_1(a136) | (~c2_1(a136)) | c0_1(a140) | c2_1(a140) | (~c3_1(a140)))) <=> ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp3 | c0_1(a140) | c3_1(a136) | (~ndr1_0) | c1_1(a136) | (~c2_1(a136)) | c2_1(a140) | (~c3_1(a140)))),
% 0.79/0.94 inference(transitivity,[status(thm)],[1949, 1947])).
% 0.79/0.94 tff(1951,plain,
% 0.79/0.94 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | (hskp3 | (~ndr1_0) | c3_1(a136) | c1_1(a136) | (~c2_1(a136)) | c0_1(a140) | c2_1(a140) | (~c3_1(a140)))),
% 0.79/0.94 inference(quant_inst,[status(thm)],[])).
% 0.79/0.94 tff(1952,plain,
% 0.79/0.94 ((~![V: $i, U: $i] : (hskp3 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c2_1(U)) | c0_1(V) | c2_1(V) | (~c3_1(V)))) | hskp3 | c0_1(a140) | c3_1(a136) | (~ndr1_0) | c1_1(a136) | (~c2_1(a136)) | c2_1(a140) | (~c3_1(a140))),
% 0.79/0.94 inference(modus_ponens,[status(thm)],[1951, 1950])).
% 0.79/0.94 tff(1953,plain,
% 0.79/0.94 (c2_1(a140)),
% 0.79/0.94 inference(unit_resolution,[status(thm)],[1952, 175, 52, 1890, 1937, 1880, 1946, 41, 1945])).
% 0.79/0.94 tff(1954,plain,
% 0.79/0.94 (~c2_1(a158)),
% 0.79/0.94 inference(unit_resolution,[status(thm)],[417, 1931])).
% 0.79/0.94 tff(1955,plain,
% 0.79/0.94 ($false),
% 0.79/0.94 inference(unit_resolution,[status(thm)],[1914, 175, 1933, 1891, 1890, 1937, 1954, 1946, 94, 1945, 1953, 1935])).
% 0.79/0.94 tff(1956,plain,(hskp13 | hskp3 | hskp21), inference(lemma,lemma(discharge,[]))).
% 0.79/0.94 tff(1957,plain,
% 0.79/0.94 (hskp13),
% 0.79/0.94 inference(unit_resolution,[status(thm)],[1956, 53, 52])).
% 0.79/0.94 tff(1958,plain,
% 0.79/0.94 (~c3_1(a144)),
% 0.79/0.94 inference(unit_resolution,[status(thm)],[928, 1957])).
% 0.79/0.94 tff(1959,plain,
% 0.79/0.94 (~c0_1(a144)),
% 0.79/0.94 inference(unit_resolution,[status(thm)],[949, 1957])).
% 0.79/0.94 tff(1960,plain,
% 0.79/0.94 (hskp6 | (~c1_1(a144))),
% 0.79/0.94 inference(unit_resolution,[status(thm)],[957, 175, 1891, 1890, 1959, 1958, 1880, 315])).
% 0.79/0.94 tff(1961,plain,
% 0.79/0.94 (~c1_1(a144)),
% 0.79/0.94 inference(unit_resolution,[status(thm)],[1960, 1878])).
% 0.79/0.94 tff(1962,plain,
% 0.79/0.94 (hskp21 | hskp16 | (~c0_1(a149))),
% 0.79/0.94 inference(unit_resolution,[status(thm)],[1293, 175, 1873, 1877, 138])).
% 0.79/0.94 tff(1963,plain,
% 0.79/0.94 (hskp16),
% 0.79/0.94 inference(unit_resolution,[status(thm)],[1962, 1876, 53])).
% 0.79/0.94 tff(1964,plain,
% 0.79/0.94 (~c2_1(a151)),
% 0.79/0.94 inference(unit_resolution,[status(thm)],[188, 1963])).
% 0.79/0.94 tff(1965,plain,
% 0.79/0.94 (c2_1(a144)),
% 0.79/0.94 inference(unit_resolution,[status(thm)],[936, 1957])).
% 0.79/0.94 tff(1966,plain,
% 0.79/0.94 (c1_1(a151)),
% 0.79/0.94 inference(unit_resolution,[status(thm)],[196, 1963])).
% 0.79/0.94 tff(1967,plain,
% 0.79/0.94 (c0_1(a151)),
% 0.79/0.94 inference(unit_resolution,[status(thm)],[231, 1963])).
% 0.79/0.94 tff(1968,plain,
% 0.79/0.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | (c2_1(a151) | c3_1(a144) | (~ndr1_0) | (~c2_1(a140)) | (~c3_1(a140)) | (~c1_1(a140)) | c1_1(a144) | (~c2_1(a144)) | (~c1_1(a151)) | (~c0_1(a151)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | c2_1(a151) | c3_1(a144) | (~ndr1_0) | (~c2_1(a140)) | (~c3_1(a140)) | (~c1_1(a140)) | c1_1(a144) | (~c2_1(a144)) | (~c1_1(a151)) | (~c0_1(a151)))),
% 0.79/0.94 inference(rewrite,[status(thm)],[])).
% 0.79/0.94 tff(1969,plain,
% 0.79/0.94 (((~ndr1_0) | (~c2_1(a140)) | (~c3_1(a140)) | (~c1_1(a140)) | c2_1(a151) | (~c1_1(a151)) | (~c0_1(a151)) | c1_1(a144) | c3_1(a144) | (~c2_1(a144))) <=> (c2_1(a151) | c3_1(a144) | (~ndr1_0) | (~c2_1(a140)) | (~c3_1(a140)) | (~c1_1(a140)) | c1_1(a144) | (~c2_1(a144)) | (~c1_1(a151)) | (~c0_1(a151)))),
% 0.79/0.94 inference(rewrite,[status(thm)],[])).
% 0.79/0.94 tff(1970,plain,
% 0.79/0.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a140)) | (~c3_1(a140)) | (~c1_1(a140)) | c2_1(a151) | (~c1_1(a151)) | (~c0_1(a151)) | c1_1(a144) | c3_1(a144) | (~c2_1(a144)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | (c2_1(a151) | c3_1(a144) | (~ndr1_0) | (~c2_1(a140)) | (~c3_1(a140)) | (~c1_1(a140)) | c1_1(a144) | (~c2_1(a144)) | (~c1_1(a151)) | (~c0_1(a151))))),
% 0.79/0.94 inference(monotonicity,[status(thm)],[1969])).
% 0.79/0.94 tff(1971,plain,
% 0.79/0.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a140)) | (~c3_1(a140)) | (~c1_1(a140)) | c2_1(a151) | (~c1_1(a151)) | (~c0_1(a151)) | c1_1(a144) | c3_1(a144) | (~c2_1(a144)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | c2_1(a151) | c3_1(a144) | (~ndr1_0) | (~c2_1(a140)) | (~c3_1(a140)) | (~c1_1(a140)) | c1_1(a144) | (~c2_1(a144)) | (~c1_1(a151)) | (~c0_1(a151)))),
% 0.79/0.94 inference(transitivity,[status(thm)],[1970, 1968])).
% 0.79/0.94 tff(1972,plain,
% 0.79/0.94 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a140)) | (~c3_1(a140)) | (~c1_1(a140)) | c2_1(a151) | (~c1_1(a151)) | (~c0_1(a151)) | c1_1(a144) | c3_1(a144) | (~c2_1(a144)))),
% 0.79/0.94 inference(quant_inst,[status(thm)],[])).
% 0.79/0.94 tff(1973,plain,
% 0.79/0.94 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | c2_1(a151) | c3_1(a144) | (~ndr1_0) | (~c2_1(a140)) | (~c3_1(a140)) | (~c1_1(a140)) | c1_1(a144) | (~c2_1(a144)) | (~c1_1(a151)) | (~c0_1(a151))),
% 0.79/0.94 inference(modus_ponens,[status(thm)],[1972, 1971])).
% 0.79/0.94 tff(1974,plain,
% 0.79/0.94 ($false),
% 0.79/0.94 inference(unit_resolution,[status(thm)],[1973, 175, 1967, 1966, 1965, 1891, 1890, 1964, 1958, 94, 1902, 1961])).
% 0.79/0.94 tff(1975,plain,(hskp14 | hskp21 | hskp3), inference(lemma,lemma(discharge,[]))).
% 0.79/0.94 tff(1976,plain,
% 0.79/0.94 (hskp14),
% 0.79/0.94 inference(unit_resolution,[status(thm)],[1975, 53, 52])).
% 0.79/0.94 tff(1977,plain,
% 0.79/0.94 (~c1_1(a145)),
% 0.79/0.94 inference(unit_resolution,[status(thm)],[495, 1976])).
% 0.79/0.94 tff(1978,plain,
% 0.79/0.94 (~c3_1(a145)),
% 0.79/0.94 inference(unit_resolution,[status(thm)],[489, 1976])).
% 0.79/0.94 tff(1979,plain,
% 0.79/0.94 (~c0_1(a145)),
% 0.79/0.94 inference(unit_resolution,[status(thm)],[508, 1976])).
% 0.79/0.94 tff(1980,plain,
% 0.79/0.94 (c0_1(a149)),
% 0.79/0.94 inference(unit_resolution,[status(thm)],[1354, 1979, 1978, 52, 1873, 1874, 1977])).
% 0.79/0.94 tff(1981,plain,
% 0.79/0.94 (~hskp6),
% 0.79/0.94 inference(unit_resolution,[status(thm)],[1929, 1979, 1874, 1877, 1977, 1978, 1980])).
% 0.79/0.94 tff(1982,plain,
% 0.79/0.94 (~c1_1(a144)),
% 0.79/0.94 inference(unit_resolution,[status(thm)],[1960, 1981])).
% 0.79/0.94 tff(1983,plain,
% 0.79/0.94 (c2_1(a140) | c1_1(a144)),
% 0.79/0.94 inference(unit_resolution,[status(thm)],[943, 175, 52, 1965, 1890, 1958, 1880, 41])).
% 0.79/0.94 tff(1984,plain,
% 0.79/0.94 (c2_1(a140)),
% 0.79/0.94 inference(unit_resolution,[status(thm)],[1983, 1982])).
% 0.79/0.94 tff(1985,plain,
% 0.79/0.94 (hskp16),
% 0.79/0.94 inference(unit_resolution,[status(thm)],[1962, 1980, 53])).
% 0.79/0.94 tff(1986,plain,
% 0.79/0.94 (~c2_1(a151)),
% 0.79/0.94 inference(unit_resolution,[status(thm)],[188, 1985])).
% 0.79/0.94 tff(1987,plain,
% 0.79/0.94 (c1_1(a151)),
% 0.79/0.94 inference(unit_resolution,[status(thm)],[196, 1985])).
% 0.79/0.94 tff(1988,plain,
% 0.79/0.94 (c0_1(a151)),
% 0.79/0.94 inference(unit_resolution,[status(thm)],[231, 1985])).
% 0.79/0.94 tff(1989,plain,
% 0.79/0.94 ($false),
% 0.79/0.94 inference(unit_resolution,[status(thm)],[1973, 175, 1988, 1987, 1965, 1891, 1890, 1986, 1958, 94, 1984, 1982])).
% 0.79/0.94 tff(1990,plain,(hskp21 | hskp3), inference(lemma,lemma(discharge,[]))).
% 0.79/0.94 tff(1991,plain,
% 0.79/0.94 (hskp21),
% 0.79/0.94 inference(unit_resolution,[status(thm)],[1990, 52])).
% 0.79/0.94 tff(1992,plain,
% 0.79/0.94 (~c2_1(a170)),
% 0.79/0.94 inference(unit_resolution,[status(thm)],[291, 1991])).
% 0.79/0.94 tff(1993,plain,
% 0.79/0.94 (~c0_1(a170)),
% 0.79/0.94 inference(unit_resolution,[status(thm)],[297, 1991])).
% 0.79/0.94 tff(1994,plain,
% 0.79/0.94 (c3_1(a170)),
% 0.79/0.94 inference(unit_resolution,[status(thm)],[322, 1991])).
% 0.79/0.94 tff(1995,plain,
% 0.79/0.94 (hskp14),
% 0.79/0.94 inference(unit_resolution,[status(thm)],[482, 175, 52, 1994, 1993, 1992, 51])).
% 0.79/0.94 tff(1996,plain,
% 0.79/0.94 (~c3_1(a145)),
% 0.79/0.94 inference(unit_resolution,[status(thm)],[489, 1995])).
% 0.79/0.94 tff(1997,plain,
% 0.79/0.94 (~c1_1(a145)),
% 0.79/0.94 inference(unit_resolution,[status(thm)],[495, 1995])).
% 0.79/0.94 tff(1998,plain,
% 0.79/0.94 (~c2_1(a145)),
% 0.79/0.94 inference(unit_resolution,[status(thm)],[502, 175, 52, 1994, 1993, 1992, 1997, 1996, 41])).
% 0.79/0.94 tff(1999,plain,
% 0.79/0.94 (~c0_1(a145)),
% 0.79/0.94 inference(unit_resolution,[status(thm)],[508, 1995])).
% 0.79/0.94 tff(2000,plain,
% 0.79/0.94 (c0_1(a149)),
% 0.79/0.94 inference(unit_resolution,[status(thm)],[1354, 1999, 1996, 52, 1873, 1874, 1997])).
% 0.79/0.94 tff(2001,plain,
% 0.79/0.94 ($false),
% 0.79/0.94 inference(unit_resolution,[status(thm)],[709, 175, 1873, 1877, 1999, 1997, 1996, 258, 2000, 1998])).
% 0.79/0.94 tff(2002,plain,(hskp3), inference(lemma,lemma(discharge,[]))).
% 0.79/0.94 tff(2003,plain,
% 0.79/0.94 (~c3_1(a128)),
% 0.79/0.94 inference(unit_resolution,[status(thm)],[1043, 2002])).
% 0.79/0.94 tff(2004,plain,
% 0.79/0.94 (~c2_1(a128)),
% 0.79/0.94 inference(unit_resolution,[status(thm)],[550, 2002])).
% 0.79/0.94 tff(2005,plain,
% 0.79/0.94 (~c0_1(a128)),
% 0.79/0.94 inference(unit_resolution,[status(thm)],[475, 2002])).
% 0.79/0.94 tff(2006,plain,
% 0.79/0.94 (^[V: $i, U: $i] : refl((hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V))) <=> (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V))))),
% 0.79/0.94 inference(bind,[status(th)],[])).
% 0.79/0.94 tff(2007,plain,
% 0.79/0.94 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.79/0.94 inference(quant_intro,[status(thm)],[2006])).
% 0.79/0.94 tff(2008,plain,
% 0.79/0.94 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V))) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.79/0.94 inference(rewrite,[status(thm)],[])).
% 0.79/0.94 tff(2009,plain,
% 0.79/0.94 (^[V: $i, U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) <=> ((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> (((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)))), rewrite((((~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U))) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V)))), ((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c1_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V)))), (((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c2_1(V)) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))) | c2_1(V)))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | (~c0_1(V))) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))), ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c2_1(V)) <=> ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V))))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c2_1(V)) | hskp16) <=> (((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V))) | hskp16))), rewrite((((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V))) | hskp16) <=> (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))), (((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c2_1(V)) | hskp16) <=> (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))))),
% 0.79/0.94 inference(bind,[status(th)],[])).
% 0.79/0.94 tff(2010,plain,
% 0.79/0.94 (![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c2_1(V)) | hskp16) <=> ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.79/0.94 inference(quant_intro,[status(thm)],[2009])).
% 0.79/0.94 tff(2011,axiom,(![V: $i, U: $i] : ((((((((~c0_1(U)) | (~c2_1(U))) | (~c3_1(U))) | (~ndr1_0)) | (~c0_1(V))) | c1_1(V)) | c2_1(V)) | hskp16)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause172')).
% 0.79/0.94 tff(2012,plain,
% 0.79/0.94 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.79/0.94 inference(modus_ponens,[status(thm)],[2011, 2010])).
% 0.79/0.94 tff(2013,plain,
% 0.79/0.94 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.79/0.94 inference(modus_ponens,[status(thm)],[2012, 2008])).
% 0.79/0.94 tff(2014,plain,(
% 0.79/0.94 ![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.79/0.94 inference(skolemize,[status(sab)],[2013])).
% 0.79/0.94 tff(2015,plain,
% 0.79/0.94 (![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))),
% 0.79/0.94 inference(modus_ponens,[status(thm)],[2014, 2007])).
% 0.79/0.94 tff(2016,plain,
% 0.79/0.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a159) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | c1_1(a128) | c1_1(a159) | (~c0_1(a159)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a159) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | c1_1(a128) | c1_1(a159) | (~c0_1(a159)))),
% 0.79/0.94 inference(rewrite,[status(thm)],[])).
% 0.79/0.94 tff(2017,plain,
% 0.79/0.94 (((~ndr1_0) | c1_1(a159) | c2_1(a159) | (~c0_1(a159)) | c3_1(a128) | c1_1(a128) | c0_1(a128) | c2_1(a128) | c1_1(a128) | c0_1(a128)) <=> (c2_1(a159) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | c1_1(a128) | c1_1(a159) | (~c0_1(a159)))),
% 0.79/0.94 inference(rewrite,[status(thm)],[])).
% 0.79/0.94 tff(2018,plain,
% 0.79/0.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a159) | c2_1(a159) | (~c0_1(a159)) | c3_1(a128) | c1_1(a128) | c0_1(a128) | c2_1(a128) | c1_1(a128) | c0_1(a128))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a159) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | c1_1(a128) | c1_1(a159) | (~c0_1(a159))))),
% 0.79/0.94 inference(monotonicity,[status(thm)],[2017])).
% 0.79/0.94 tff(2019,plain,
% 0.79/0.94 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a159) | c2_1(a159) | (~c0_1(a159)) | c3_1(a128) | c1_1(a128) | c0_1(a128) | c2_1(a128) | c1_1(a128) | c0_1(a128))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a159) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | c1_1(a128) | c1_1(a159) | (~c0_1(a159)))),
% 0.79/0.94 inference(transitivity,[status(thm)],[2018, 2016])).
% 0.79/0.94 tff(2020,plain,
% 0.79/0.94 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a159) | c2_1(a159) | (~c0_1(a159)) | c3_1(a128) | c1_1(a128) | c0_1(a128) | c2_1(a128) | c1_1(a128) | c0_1(a128))),
% 0.79/0.94 inference(quant_inst,[status(thm)],[])).
% 0.79/0.94 tff(2021,plain,
% 0.79/0.94 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a159) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | c1_1(a128) | c1_1(a159) | (~c0_1(a159))),
% 0.79/0.94 inference(modus_ponens,[status(thm)],[2020, 2019])).
% 0.79/0.94 tff(2022,plain,
% 0.79/0.94 (c1_1(a128)),
% 0.79/0.94 inference(unit_resolution,[status(thm)],[2021, 175, 1821, 1813, 2005, 2004, 2003, 460, 1862])).
% 0.79/0.95 tff(2023,plain,
% 0.79/0.95 (^[U: $i] : refl((hskp27 | hskp15 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U))) <=> (hskp27 | hskp15 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U))))),
% 0.79/0.95 inference(bind,[status(th)],[])).
% 0.79/0.95 tff(2024,plain,
% 0.79/0.95 (![U: $i] : (hskp27 | hskp15 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp27 | hskp15 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))),
% 0.79/0.95 inference(quant_intro,[status(thm)],[2023])).
% 0.79/0.95 tff(2025,plain,
% 0.79/0.95 (![U: $i] : (hskp27 | hskp15 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U))) <=> ![U: $i] : (hskp27 | hskp15 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))),
% 0.79/0.95 inference(rewrite,[status(thm)],[])).
% 0.79/0.95 tff(2026,plain,
% 0.79/0.95 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c1_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) <=> (((~ndr1_0) | (~c1_1(U))) | c0_1(U)))), rewrite((((~ndr1_0) | (~c1_1(U))) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U)))), ((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) <=> ((~ndr1_0) | c0_1(U) | (~c1_1(U))))), (((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c0_1(U) | (~c1_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c0_1(U) | (~c1_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))), (((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U))))), ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp27) <=> (((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U))) | hskp27))), rewrite((((~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U))) | hskp27) <=> (hskp27 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))), ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp27) <=> (hskp27 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U))))), (((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp27) | hskp15) <=> ((hskp27 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U))) | hskp15))), rewrite(((hskp27 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U))) | hskp15) <=> (hskp27 | hskp15 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))), (((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp27) | hskp15) <=> (hskp27 | hskp15 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))))),
% 0.79/0.95 inference(bind,[status(th)],[])).
% 0.79/0.95 tff(2027,plain,
% 0.79/0.95 (![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp27) | hskp15) <=> ![U: $i] : (hskp27 | hskp15 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))),
% 0.79/0.95 inference(quant_intro,[status(thm)],[2026])).
% 0.79/0.95 tff(2028,axiom,(![U: $i] : ((((((~c1_1(U)) | (~ndr1_0)) | c0_1(U)) | c3_1(U)) | hskp27) | hskp15)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause139')).
% 0.79/0.95 tff(2029,plain,
% 0.79/0.95 (![U: $i] : (hskp27 | hskp15 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))),
% 0.79/0.95 inference(modus_ponens,[status(thm)],[2028, 2027])).
% 0.79/0.95 tff(2030,plain,
% 0.79/0.95 (![U: $i] : (hskp27 | hskp15 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))),
% 0.79/0.95 inference(modus_ponens,[status(thm)],[2029, 2025])).
% 0.79/0.95 tff(2031,plain,(
% 0.79/0.95 ![U: $i] : (hskp27 | hskp15 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))),
% 0.79/0.95 inference(skolemize,[status(sab)],[2030])).
% 0.79/0.95 tff(2032,plain,
% 0.79/0.95 (![U: $i] : (hskp27 | hskp15 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))),
% 0.79/0.95 inference(modus_ponens,[status(thm)],[2031, 2024])).
% 0.79/0.95 tff(2033,plain,
% 0.79/0.95 (((~![U: $i] : (hskp27 | hskp15 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp27 | hskp15 | c0_1(a128) | c3_1(a128) | (~ndr1_0) | (~c1_1(a128)))) <=> ((~![U: $i] : (hskp27 | hskp15 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))) | hskp27 | hskp15 | c0_1(a128) | c3_1(a128) | (~ndr1_0) | (~c1_1(a128)))),
% 0.79/0.95 inference(rewrite,[status(thm)],[])).
% 0.79/0.95 tff(2034,plain,
% 0.79/0.95 ((hskp27 | hskp15 | (~ndr1_0) | c3_1(a128) | c0_1(a128) | (~c1_1(a128))) <=> (hskp27 | hskp15 | c0_1(a128) | c3_1(a128) | (~ndr1_0) | (~c1_1(a128)))),
% 0.79/0.95 inference(rewrite,[status(thm)],[])).
% 0.79/0.95 tff(2035,plain,
% 0.79/0.95 (((~![U: $i] : (hskp27 | hskp15 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp27 | hskp15 | (~ndr1_0) | c3_1(a128) | c0_1(a128) | (~c1_1(a128)))) <=> ((~![U: $i] : (hskp27 | hskp15 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp27 | hskp15 | c0_1(a128) | c3_1(a128) | (~ndr1_0) | (~c1_1(a128))))),
% 0.79/0.95 inference(monotonicity,[status(thm)],[2034])).
% 0.79/0.95 tff(2036,plain,
% 0.79/0.95 (((~![U: $i] : (hskp27 | hskp15 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp27 | hskp15 | (~ndr1_0) | c3_1(a128) | c0_1(a128) | (~c1_1(a128)))) <=> ((~![U: $i] : (hskp27 | hskp15 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))) | hskp27 | hskp15 | c0_1(a128) | c3_1(a128) | (~ndr1_0) | (~c1_1(a128)))),
% 0.79/0.95 inference(transitivity,[status(thm)],[2035, 2033])).
% 0.79/0.95 tff(2037,plain,
% 0.79/0.95 ((~![U: $i] : (hskp27 | hskp15 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))) | (hskp27 | hskp15 | (~ndr1_0) | c3_1(a128) | c0_1(a128) | (~c1_1(a128)))),
% 0.79/0.95 inference(quant_inst,[status(thm)],[])).
% 0.79/0.95 tff(2038,plain,
% 0.79/0.95 ((~![U: $i] : (hskp27 | hskp15 | (~ndr1_0) | c3_1(U) | c0_1(U) | (~c1_1(U)))) | hskp27 | hskp15 | c0_1(a128) | c3_1(a128) | (~ndr1_0) | (~c1_1(a128))),
% 0.79/0.95 inference(modus_ponens,[status(thm)],[2037, 2036])).
% 0.79/0.95 tff(2039,plain,
% 0.79/0.95 (hskp27 | hskp15 | (~c1_1(a128))),
% 0.79/0.95 inference(unit_resolution,[status(thm)],[2038, 175, 2005, 2003, 2032])).
% 0.79/0.95 tff(2040,plain,
% 0.79/0.95 (hskp27),
% 0.79/0.95 inference(unit_resolution,[status(thm)],[2039, 2022, 74])).
% 0.79/0.95 tff(2041,plain,
% 0.79/0.95 (c3_1(a137)),
% 0.79/0.95 inference(unit_resolution,[status(thm)],[1146, 2040])).
% 0.79/0.95 tff(2042,plain,
% 0.79/0.95 (c2_1(a137)),
% 0.79/0.95 inference(unit_resolution,[status(thm)],[1154, 2040])).
% 0.79/0.95 tff(2043,assumption,(hskp16), introduced(assumption)).
% 0.79/0.95 tff(2044,plain,
% 0.79/0.95 (~c2_1(a151)),
% 0.79/0.95 inference(unit_resolution,[status(thm)],[188, 2043])).
% 0.79/0.95 tff(2045,plain,
% 0.79/0.95 (c1_1(a151)),
% 0.79/0.95 inference(unit_resolution,[status(thm)],[196, 2043])).
% 0.79/0.95 tff(2046,plain,
% 0.79/0.95 (c0_1(a151)),
% 0.79/0.95 inference(unit_resolution,[status(thm)],[231, 2043])).
% 0.79/0.95 tff(2047,plain,
% 0.79/0.95 ($false),
% 0.79/0.95 inference(unit_resolution,[status(thm)],[238, 175, 74, 2046, 2045, 2044, 63])).
% 0.79/0.95 tff(2048,plain,((~hskp16) | hskp15), inference(lemma,lemma(discharge,[]))).
% 0.79/0.95 tff(2049,plain,
% 0.79/0.95 (~hskp16),
% 0.79/0.95 inference(unit_resolution,[status(thm)],[2048, 74])).
% 0.79/0.95 tff(2050,plain,
% 0.79/0.95 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp16 | c2_1(a159) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c0_1(a137)) | c1_1(a159) | (~c0_1(a159)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp16 | c2_1(a159) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c0_1(a137)) | c1_1(a159) | (~c0_1(a159)))),
% 0.79/0.95 inference(rewrite,[status(thm)],[])).
% 0.79/0.95 tff(2051,plain,
% 0.79/0.95 ((hskp16 | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c0_1(a137)) | c1_1(a159) | c2_1(a159) | (~c0_1(a159))) <=> (hskp16 | c2_1(a159) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c0_1(a137)) | c1_1(a159) | (~c0_1(a159)))),
% 0.79/0.95 inference(rewrite,[status(thm)],[])).
% 0.79/0.95 tff(2052,plain,
% 0.79/0.95 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp16 | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c0_1(a137)) | c1_1(a159) | c2_1(a159) | (~c0_1(a159)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp16 | c2_1(a159) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c0_1(a137)) | c1_1(a159) | (~c0_1(a159))))),
% 0.79/0.95 inference(monotonicity,[status(thm)],[2051])).
% 0.79/0.95 tff(2053,plain,
% 0.79/0.95 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp16 | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c0_1(a137)) | c1_1(a159) | c2_1(a159) | (~c0_1(a159)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp16 | c2_1(a159) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c0_1(a137)) | c1_1(a159) | (~c0_1(a159)))),
% 0.79/0.95 inference(transitivity,[status(thm)],[2052, 2050])).
% 0.79/0.95 tff(2054,plain,
% 0.79/0.95 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp16 | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c0_1(a137)) | c1_1(a159) | c2_1(a159) | (~c0_1(a159)))),
% 0.79/0.95 inference(quant_inst,[status(thm)],[])).
% 0.79/0.95 tff(2055,plain,
% 0.79/0.95 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp16 | c2_1(a159) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c0_1(a137)) | c1_1(a159) | (~c0_1(a159))),
% 0.79/0.95 inference(modus_ponens,[status(thm)],[2054, 2053])).
% 0.79/0.95 tff(2056,plain,
% 0.79/0.95 (~c0_1(a137)),
% 0.79/0.95 inference(unit_resolution,[status(thm)],[2055, 175, 2049, 2042, 2041, 1821, 1813, 2015, 1862])).
% 0.79/0.95 tff(2057,plain,
% 0.79/0.95 (c1_1(a137)),
% 0.79/0.95 inference(unit_resolution,[status(thm)],[1162, 2040])).
% 0.79/0.95 tff(2058,plain,
% 0.79/0.95 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | c0_1(a128) | c3_1(a128) | (~ndr1_0) | (~c3_1(a137)) | (~c1_1(a137)) | c0_1(a137) | (~c1_1(a128)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp6 | c0_1(a128) | c3_1(a128) | (~ndr1_0) | (~c3_1(a137)) | (~c1_1(a137)) | c0_1(a137) | (~c1_1(a128)))),
% 0.79/0.95 inference(rewrite,[status(thm)],[])).
% 0.79/0.95 tff(2059,plain,
% 0.79/0.95 ((hskp6 | (~ndr1_0) | c0_1(a137) | (~c3_1(a137)) | (~c1_1(a137)) | c3_1(a128) | c0_1(a128) | (~c1_1(a128))) <=> (hskp6 | c0_1(a128) | c3_1(a128) | (~ndr1_0) | (~c3_1(a137)) | (~c1_1(a137)) | c0_1(a137) | (~c1_1(a128)))),
% 0.79/0.95 inference(rewrite,[status(thm)],[])).
% 0.79/0.95 tff(2060,plain,
% 0.79/0.95 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | (~ndr1_0) | c0_1(a137) | (~c3_1(a137)) | (~c1_1(a137)) | c3_1(a128) | c0_1(a128) | (~c1_1(a128)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | c0_1(a128) | c3_1(a128) | (~ndr1_0) | (~c3_1(a137)) | (~c1_1(a137)) | c0_1(a137) | (~c1_1(a128))))),
% 0.79/0.95 inference(monotonicity,[status(thm)],[2059])).
% 0.79/0.95 tff(2061,plain,
% 0.79/0.95 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | (~ndr1_0) | c0_1(a137) | (~c3_1(a137)) | (~c1_1(a137)) | c3_1(a128) | c0_1(a128) | (~c1_1(a128)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp6 | c0_1(a128) | c3_1(a128) | (~ndr1_0) | (~c3_1(a137)) | (~c1_1(a137)) | c0_1(a137) | (~c1_1(a128)))),
% 0.79/0.95 inference(transitivity,[status(thm)],[2060, 2058])).
% 0.79/0.95 tff(2062,plain,
% 0.79/0.95 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | (~ndr1_0) | c0_1(a137) | (~c3_1(a137)) | (~c1_1(a137)) | c3_1(a128) | c0_1(a128) | (~c1_1(a128)))),
% 0.79/0.95 inference(quant_inst,[status(thm)],[])).
% 0.79/0.95 tff(2063,plain,
% 0.79/0.95 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp6 | c0_1(a128) | c3_1(a128) | (~ndr1_0) | (~c3_1(a137)) | (~c1_1(a137)) | c0_1(a137) | (~c1_1(a128))),
% 0.79/0.95 inference(modus_ponens,[status(thm)],[2062, 2061])).
% 0.79/0.95 tff(2064,plain,
% 0.79/0.95 (hskp6),
% 0.79/0.95 inference(unit_resolution,[status(thm)],[2063, 175, 2057, 2041, 2005, 2003, 315, 2022, 2056])).
% 0.79/0.95 tff(2065,plain,
% 0.79/0.95 (~c2_1(a133)),
% 0.79/0.95 inference(unit_resolution,[status(thm)],[336, 2064])).
% 0.79/0.95 tff(2066,plain,
% 0.79/0.95 (~c1_1(a133)),
% 0.79/0.95 inference(unit_resolution,[status(thm)],[342, 2064])).
% 0.79/0.95 tff(2067,plain,
% 0.79/0.95 (~c0_1(a133)),
% 0.79/0.95 inference(unit_resolution,[status(thm)],[348, 2064])).
% 0.79/0.95 tff(2068,assumption,(~c0_1(a137)), introduced(assumption)).
% 0.79/0.95 tff(2069,assumption,(~c1_1(a159)), introduced(assumption)).
% 0.79/0.95 tff(2070,assumption,(~hskp4), introduced(assumption)).
% 0.79/0.95 tff(2071,plain,
% 0.79/0.95 (^[U: $i] : refl((hskp5 | hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))) <=> (hskp5 | hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))))),
% 0.79/0.95 inference(bind,[status(th)],[])).
% 0.79/0.95 tff(2072,plain,
% 0.79/0.95 (![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))),
% 0.79/0.95 inference(quant_intro,[status(thm)],[2071])).
% 0.79/0.95 tff(2073,plain,
% 0.79/0.95 (![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))) <=> ![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))),
% 0.79/0.95 inference(rewrite,[status(thm)],[])).
% 0.79/0.95 tff(2074,plain,
% 0.79/0.95 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~c0_1(U)) | (~ndr1_0)) <=> ((~ndr1_0) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> (((~ndr1_0) | (~c0_1(U))) | c1_1(U)))), rewrite((((~ndr1_0) | (~c0_1(U))) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U)))), ((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) <=> ((~ndr1_0) | c1_1(U) | (~c0_1(U))))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> (((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c3_1(U)))), rewrite((((~ndr1_0) | c1_1(U) | (~c0_1(U))) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))), (((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) <=> ((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp4) <=> (((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))) | hskp4))), rewrite((((~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))) | hskp4) <=> (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))), ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp4) <=> (hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp4) | hskp5) <=> ((hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))) | hskp5))), rewrite(((hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U))) | hskp5) <=> (hskp5 | hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))), (((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp4) | hskp5) <=> (hskp5 | hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))))),
% 0.79/0.95 inference(bind,[status(th)],[])).
% 0.79/0.95 tff(2075,plain,
% 0.79/0.95 (![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp4) | hskp5) <=> ![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))),
% 0.79/0.95 inference(quant_intro,[status(thm)],[2074])).
% 0.79/0.95 tff(2076,axiom,(![U: $i] : ((((((~c0_1(U)) | (~ndr1_0)) | c1_1(U)) | c3_1(U)) | hskp4) | hskp5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause143')).
% 0.79/0.95 tff(2077,plain,
% 0.79/0.95 (![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))),
% 0.79/0.95 inference(modus_ponens,[status(thm)],[2076, 2075])).
% 0.79/0.95 tff(2078,plain,
% 0.79/0.95 (![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))),
% 0.79/0.95 inference(modus_ponens,[status(thm)],[2077, 2073])).
% 0.79/0.95 tff(2079,plain,(
% 0.79/0.95 ![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))),
% 0.79/0.95 inference(skolemize,[status(sab)],[2078])).
% 0.79/0.95 tff(2080,plain,
% 0.79/0.95 (![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))),
% 0.79/0.95 inference(modus_ponens,[status(thm)],[2079, 2072])).
% 0.79/0.95 tff(2081,plain,
% 0.79/0.95 (((~![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp5 | hskp4 | c3_1(a159) | (~ndr1_0) | c1_1(a159) | (~c0_1(a159)))) <=> ((~![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | hskp5 | hskp4 | c3_1(a159) | (~ndr1_0) | c1_1(a159) | (~c0_1(a159)))),
% 0.79/0.95 inference(rewrite,[status(thm)],[])).
% 0.79/0.95 tff(2082,plain,
% 0.79/0.95 ((hskp5 | hskp4 | (~ndr1_0) | c3_1(a159) | c1_1(a159) | (~c0_1(a159))) <=> (hskp5 | hskp4 | c3_1(a159) | (~ndr1_0) | c1_1(a159) | (~c0_1(a159)))),
% 0.79/0.95 inference(rewrite,[status(thm)],[])).
% 0.79/0.95 tff(2083,plain,
% 0.79/0.95 (((~![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp5 | hskp4 | (~ndr1_0) | c3_1(a159) | c1_1(a159) | (~c0_1(a159)))) <=> ((~![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp5 | hskp4 | c3_1(a159) | (~ndr1_0) | c1_1(a159) | (~c0_1(a159))))),
% 0.79/0.95 inference(monotonicity,[status(thm)],[2082])).
% 0.79/0.95 tff(2084,plain,
% 0.79/0.95 (((~![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp5 | hskp4 | (~ndr1_0) | c3_1(a159) | c1_1(a159) | (~c0_1(a159)))) <=> ((~![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | hskp5 | hskp4 | c3_1(a159) | (~ndr1_0) | c1_1(a159) | (~c0_1(a159)))),
% 0.79/0.95 inference(transitivity,[status(thm)],[2083, 2081])).
% 0.79/0.95 tff(2085,plain,
% 0.79/0.95 ((~![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp5 | hskp4 | (~ndr1_0) | c3_1(a159) | c1_1(a159) | (~c0_1(a159)))),
% 0.79/0.95 inference(quant_inst,[status(thm)],[])).
% 0.79/0.95 tff(2086,plain,
% 0.79/0.95 ((~![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | hskp5 | hskp4 | c3_1(a159) | (~ndr1_0) | c1_1(a159) | (~c0_1(a159))),
% 0.79/0.95 inference(modus_ponens,[status(thm)],[2085, 2084])).
% 0.79/0.95 tff(2087,plain,
% 0.79/0.95 (hskp5 | hskp4 | c1_1(a159)),
% 0.79/0.95 inference(unit_resolution,[status(thm)],[2086, 175, 1821, 1807, 2080])).
% 0.79/0.95 tff(2088,plain,
% 0.79/0.95 (hskp5),
% 0.79/0.95 inference(unit_resolution,[status(thm)],[2087, 2070, 2069])).
% 0.79/0.95 tff(2089,plain,
% 0.79/0.95 (((~hskp5) | (~c2_1(a131))) <=> ((~hskp5) | (~c2_1(a131)))),
% 0.79/0.95 inference(rewrite,[status(thm)],[])).
% 0.79/0.95 tff(2090,plain,
% 0.79/0.95 (((~c2_1(a131)) | (~hskp5)) <=> ((~hskp5) | (~c2_1(a131)))),
% 0.79/0.95 inference(rewrite,[status(thm)],[])).
% 0.79/0.95 tff(2091,axiom,((~c2_1(a131)) | (~hskp5)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause121')).
% 0.79/0.95 tff(2092,plain,
% 0.79/0.95 ((~hskp5) | (~c2_1(a131))),
% 0.79/0.95 inference(modus_ponens,[status(thm)],[2091, 2090])).
% 0.79/0.95 tff(2093,plain,
% 0.79/0.95 ((~hskp5) | (~c2_1(a131))),
% 0.79/0.95 inference(modus_ponens,[status(thm)],[2092, 2089])).
% 0.79/0.95 tff(2094,plain,
% 0.79/0.95 (~c2_1(a131)),
% 0.79/0.95 inference(unit_resolution,[status(thm)],[2093, 2088])).
% 0.79/0.95 tff(2095,assumption,(~c2_1(a133)), introduced(assumption)).
% 0.79/0.95 tff(2096,assumption,(~c1_1(a133)), introduced(assumption)).
% 0.79/0.95 tff(2097,plain,
% 0.79/0.95 (((~hskp5) | c3_1(a131)) <=> ((~hskp5) | c3_1(a131))),
% 0.79/0.95 inference(rewrite,[status(thm)],[])).
% 0.79/0.95 tff(2098,axiom,((~hskp5) | c3_1(a131)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause76')).
% 0.79/0.95 tff(2099,plain,
% 0.79/0.95 ((~hskp5) | c3_1(a131)),
% 0.79/0.95 inference(modus_ponens,[status(thm)],[2098, 2097])).
% 0.79/0.95 tff(2100,plain,
% 0.79/0.95 ((~hskp5) | c3_1(a131)),
% 0.79/0.95 inference(modus_ponens,[status(thm)],[2099, 2097])).
% 0.79/0.95 tff(2101,plain,
% 0.79/0.95 ((~hskp5) | c3_1(a131)),
% 0.79/0.95 inference(modus_ponens,[status(thm)],[2100, 2097])).
% 0.79/0.95 tff(2102,plain,
% 0.79/0.95 ((~hskp5) | c3_1(a131)),
% 0.79/0.95 inference(modus_ponens,[status(thm)],[2101, 2097])).
% 0.79/0.95 tff(2103,plain,
% 0.79/0.95 ((~hskp5) | c3_1(a131)),
% 0.79/0.95 inference(modus_ponens,[status(thm)],[2102, 2097])).
% 0.79/0.95 tff(2104,plain,
% 0.79/0.95 (c3_1(a131)),
% 0.79/0.95 inference(unit_resolution,[status(thm)],[2103, 2088])).
% 0.79/0.95 tff(2105,plain,
% 0.79/0.95 (((~hskp5) | c1_1(a131)) <=> ((~hskp5) | c1_1(a131))),
% 0.79/0.95 inference(rewrite,[status(thm)],[])).
% 0.79/0.95 tff(2106,axiom,((~hskp5) | c1_1(a131)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause75')).
% 0.79/0.95 tff(2107,plain,
% 0.79/0.95 ((~hskp5) | c1_1(a131)),
% 0.79/0.95 inference(modus_ponens,[status(thm)],[2106, 2105])).
% 0.79/0.95 tff(2108,plain,
% 0.79/0.95 ((~hskp5) | c1_1(a131)),
% 0.79/0.95 inference(modus_ponens,[status(thm)],[2107, 2105])).
% 0.79/0.95 tff(2109,plain,
% 0.79/0.95 ((~hskp5) | c1_1(a131)),
% 0.79/0.95 inference(modus_ponens,[status(thm)],[2108, 2105])).
% 0.79/0.95 tff(2110,plain,
% 0.79/0.95 ((~hskp5) | c1_1(a131)),
% 0.79/0.95 inference(modus_ponens,[status(thm)],[2109, 2105])).
% 0.79/0.95 tff(2111,plain,
% 0.79/0.95 ((~hskp5) | c1_1(a131)),
% 0.79/0.95 inference(modus_ponens,[status(thm)],[2110, 2105])).
% 0.79/0.95 tff(2112,plain,
% 0.79/0.95 (c1_1(a131)),
% 0.79/0.95 inference(unit_resolution,[status(thm)],[2111, 2088])).
% 0.79/0.95 tff(2113,assumption,(c3_1(a137)), introduced(assumption)).
% 0.79/0.95 tff(2114,assumption,(c2_1(a137)), introduced(assumption)).
% 0.79/0.95 tff(2115,plain,
% 0.79/0.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | (c1_1(a133) | c2_1(a133) | c2_1(a131) | (~ndr1_0) | (~c3_1(a131)) | (~c1_1(a131)) | (~c2_1(a137)) | (~c3_1(a137)) | c0_1(a137) | (~c3_1(a133)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c1_1(a133) | c2_1(a133) | c2_1(a131) | (~ndr1_0) | (~c3_1(a131)) | (~c1_1(a131)) | (~c2_1(a137)) | (~c3_1(a137)) | c0_1(a137) | (~c3_1(a133)))),
% 0.79/0.95 inference(rewrite,[status(thm)],[])).
% 0.79/0.95 tff(2116,plain,
% 0.79/0.95 (((~ndr1_0) | c2_1(a131) | (~c3_1(a131)) | (~c1_1(a131)) | c1_1(a133) | c2_1(a133) | (~c3_1(a133)) | c0_1(a137) | (~c2_1(a137)) | (~c3_1(a137))) <=> (c1_1(a133) | c2_1(a133) | c2_1(a131) | (~ndr1_0) | (~c3_1(a131)) | (~c1_1(a131)) | (~c2_1(a137)) | (~c3_1(a137)) | c0_1(a137) | (~c3_1(a133)))),
% 0.79/0.95 inference(rewrite,[status(thm)],[])).
% 0.79/0.95 tff(2117,plain,
% 0.79/0.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a131) | (~c3_1(a131)) | (~c1_1(a131)) | c1_1(a133) | c2_1(a133) | (~c3_1(a133)) | c0_1(a137) | (~c2_1(a137)) | (~c3_1(a137)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | (c1_1(a133) | c2_1(a133) | c2_1(a131) | (~ndr1_0) | (~c3_1(a131)) | (~c1_1(a131)) | (~c2_1(a137)) | (~c3_1(a137)) | c0_1(a137) | (~c3_1(a133))))),
% 0.79/0.95 inference(monotonicity,[status(thm)],[2116])).
% 0.79/0.95 tff(2118,plain,
% 0.79/0.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a131) | (~c3_1(a131)) | (~c1_1(a131)) | c1_1(a133) | c2_1(a133) | (~c3_1(a133)) | c0_1(a137) | (~c2_1(a137)) | (~c3_1(a137)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c1_1(a133) | c2_1(a133) | c2_1(a131) | (~ndr1_0) | (~c3_1(a131)) | (~c1_1(a131)) | (~c2_1(a137)) | (~c3_1(a137)) | c0_1(a137) | (~c3_1(a133)))),
% 0.79/0.95 inference(transitivity,[status(thm)],[2117, 2115])).
% 0.79/0.95 tff(2119,plain,
% 0.79/0.95 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | ((~ndr1_0) | c2_1(a131) | (~c3_1(a131)) | (~c1_1(a131)) | c1_1(a133) | c2_1(a133) | (~c3_1(a133)) | c0_1(a137) | (~c2_1(a137)) | (~c3_1(a137)))),
% 0.79/0.95 inference(quant_inst,[status(thm)],[])).
% 0.79/0.95 tff(2120,plain,
% 0.79/0.95 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c1_1(V) | c2_1(V) | (~c3_1(V)) | c0_1(W) | (~c2_1(W)) | (~c3_1(W)))) | c1_1(a133) | c2_1(a133) | c2_1(a131) | (~ndr1_0) | (~c3_1(a131)) | (~c1_1(a131)) | (~c2_1(a137)) | (~c3_1(a137)) | c0_1(a137) | (~c3_1(a133))),
% 0.79/0.95 inference(modus_ponens,[status(thm)],[2119, 2118])).
% 0.79/0.95 tff(2121,plain,
% 0.79/0.95 (~c3_1(a133)),
% 0.79/0.95 inference(unit_resolution,[status(thm)],[2120, 175, 2114, 2113, 2112, 2104, 2096, 2095, 2094, 214, 2068])).
% 0.79/0.95 tff(2122,assumption,(~c0_1(a133)), introduced(assumption)).
% 0.79/0.95 tff(2123,plain,
% 0.79/0.95 (^[U: $i] : refl((hskp24 | hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> (hskp24 | hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))))),
% 0.79/0.95 inference(bind,[status(th)],[])).
% 0.79/0.95 tff(2124,plain,
% 0.79/0.95 (![U: $i] : (hskp24 | hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp24 | hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.79/0.95 inference(quant_intro,[status(thm)],[2123])).
% 0.79/0.95 tff(2125,plain,
% 0.79/0.95 (![U: $i] : (hskp24 | hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) <=> ![U: $i] : (hskp24 | hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.79/0.95 inference(rewrite,[status(thm)],[])).
% 0.79/0.95 tff(2126,plain,
% 0.79/0.95 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c1_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))), (((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp4) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp4))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp4) <=> (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))), ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp4) <=> (hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp4) | hskp24) <=> ((hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp24))), rewrite(((hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U))) | hskp24) <=> (hskp24 | hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))), (((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp4) | hskp24) <=> (hskp24 | hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))))),
% 0.79/0.95 inference(bind,[status(th)],[])).
% 0.79/0.95 tff(2127,plain,
% 0.79/0.95 (![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp4) | hskp24) <=> ![U: $i] : (hskp24 | hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.79/0.95 inference(quant_intro,[status(thm)],[2126])).
% 0.79/0.95 tff(2128,axiom,(![U: $i] : ((((((~c1_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp4) | hskp24)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause153')).
% 0.79/0.95 tff(2129,plain,
% 0.79/0.95 (![U: $i] : (hskp24 | hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.79/0.95 inference(modus_ponens,[status(thm)],[2128, 2127])).
% 0.79/0.95 tff(2130,plain,
% 0.79/0.95 (![U: $i] : (hskp24 | hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.79/0.95 inference(modus_ponens,[status(thm)],[2129, 2125])).
% 0.79/0.95 tff(2131,plain,(
% 0.79/0.95 ![U: $i] : (hskp24 | hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.79/0.95 inference(skolemize,[status(sab)],[2130])).
% 0.79/0.95 tff(2132,plain,
% 0.79/0.95 (![U: $i] : (hskp24 | hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))),
% 0.79/0.95 inference(modus_ponens,[status(thm)],[2131, 2124])).
% 0.79/0.95 tff(2133,plain,
% 0.79/0.95 (((~![U: $i] : (hskp24 | hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp24 | hskp4 | c2_1(a131) | (~ndr1_0) | (~c3_1(a131)) | (~c1_1(a131)))) <=> ((~![U: $i] : (hskp24 | hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp24 | hskp4 | c2_1(a131) | (~ndr1_0) | (~c3_1(a131)) | (~c1_1(a131)))),
% 0.79/0.95 inference(rewrite,[status(thm)],[])).
% 0.79/0.95 tff(2134,plain,
% 0.79/0.95 ((hskp24 | hskp4 | (~ndr1_0) | c2_1(a131) | (~c3_1(a131)) | (~c1_1(a131))) <=> (hskp24 | hskp4 | c2_1(a131) | (~ndr1_0) | (~c3_1(a131)) | (~c1_1(a131)))),
% 0.79/0.95 inference(rewrite,[status(thm)],[])).
% 0.79/0.95 tff(2135,plain,
% 0.79/0.95 (((~![U: $i] : (hskp24 | hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp24 | hskp4 | (~ndr1_0) | c2_1(a131) | (~c3_1(a131)) | (~c1_1(a131)))) <=> ((~![U: $i] : (hskp24 | hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp24 | hskp4 | c2_1(a131) | (~ndr1_0) | (~c3_1(a131)) | (~c1_1(a131))))),
% 0.79/0.95 inference(monotonicity,[status(thm)],[2134])).
% 0.79/0.95 tff(2136,plain,
% 0.79/0.95 (((~![U: $i] : (hskp24 | hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp24 | hskp4 | (~ndr1_0) | c2_1(a131) | (~c3_1(a131)) | (~c1_1(a131)))) <=> ((~![U: $i] : (hskp24 | hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp24 | hskp4 | c2_1(a131) | (~ndr1_0) | (~c3_1(a131)) | (~c1_1(a131)))),
% 0.79/0.95 inference(transitivity,[status(thm)],[2135, 2133])).
% 0.79/0.95 tff(2137,plain,
% 0.79/0.95 ((~![U: $i] : (hskp24 | hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | (hskp24 | hskp4 | (~ndr1_0) | c2_1(a131) | (~c3_1(a131)) | (~c1_1(a131)))),
% 0.79/0.95 inference(quant_inst,[status(thm)],[])).
% 0.79/0.95 tff(2138,plain,
% 0.79/0.95 ((~![U: $i] : (hskp24 | hskp4 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)))) | hskp24 | hskp4 | c2_1(a131) | (~ndr1_0) | (~c3_1(a131)) | (~c1_1(a131))),
% 0.79/0.95 inference(modus_ponens,[status(thm)],[2137, 2136])).
% 0.79/0.95 tff(2139,plain,
% 0.79/0.95 (hskp24),
% 0.79/0.95 inference(unit_resolution,[status(thm)],[2138, 175, 2070, 2112, 2104, 2094, 2132])).
% 0.79/0.95 tff(2140,plain,
% 0.79/0.95 (((~hskp24) | (~c2_1(a183))) <=> ((~hskp24) | (~c2_1(a183)))),
% 0.79/0.95 inference(rewrite,[status(thm)],[])).
% 0.79/0.95 tff(2141,plain,
% 0.79/0.95 (((~c2_1(a183)) | (~hskp24)) <=> ((~hskp24) | (~c2_1(a183)))),
% 0.79/0.95 inference(rewrite,[status(thm)],[])).
% 0.79/0.95 tff(2142,axiom,((~c2_1(a183)) | (~hskp24)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause89')).
% 0.79/0.95 tff(2143,plain,
% 0.79/0.95 ((~hskp24) | (~c2_1(a183))),
% 0.79/0.95 inference(modus_ponens,[status(thm)],[2142, 2141])).
% 0.79/0.95 tff(2144,plain,
% 0.79/0.95 ((~hskp24) | (~c2_1(a183))),
% 0.79/0.95 inference(modus_ponens,[status(thm)],[2143, 2140])).
% 0.79/0.95 tff(2145,plain,
% 0.79/0.95 (~c2_1(a183)),
% 0.79/0.95 inference(unit_resolution,[status(thm)],[2144, 2139])).
% 0.79/0.95 tff(2146,plain,
% 0.79/0.95 (((~hskp24) | (~c1_1(a183))) <=> ((~hskp24) | (~c1_1(a183)))),
% 0.79/0.95 inference(rewrite,[status(thm)],[])).
% 0.79/0.95 tff(2147,plain,
% 0.79/0.95 (((~c1_1(a183)) | (~hskp24)) <=> ((~hskp24) | (~c1_1(a183)))),
% 0.79/0.95 inference(rewrite,[status(thm)],[])).
% 0.79/0.95 tff(2148,axiom,((~c1_1(a183)) | (~hskp24)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause88')).
% 0.79/0.95 tff(2149,plain,
% 0.79/0.95 ((~hskp24) | (~c1_1(a183))),
% 0.79/0.95 inference(modus_ponens,[status(thm)],[2148, 2147])).
% 0.79/0.95 tff(2150,plain,
% 0.79/0.95 ((~hskp24) | (~c1_1(a183))),
% 0.79/0.95 inference(modus_ponens,[status(thm)],[2149, 2146])).
% 0.79/0.95 tff(2151,plain,
% 0.79/0.95 (~c1_1(a183)),
% 0.79/0.95 inference(unit_resolution,[status(thm)],[2150, 2139])).
% 0.79/0.95 tff(2152,plain,
% 0.79/0.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a183) | c2_1(a183) | c0_1(a133) | c1_1(a133) | c2_1(a133) | (~ndr1_0) | c3_1(a133) | (~c0_1(a183)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a183) | c2_1(a183) | c0_1(a133) | c1_1(a133) | c2_1(a133) | (~ndr1_0) | c3_1(a133) | (~c0_1(a183)))),
% 0.79/0.95 inference(rewrite,[status(thm)],[])).
% 0.79/0.95 tff(2153,plain,
% 0.79/0.95 (((~ndr1_0) | c1_1(a183) | c2_1(a183) | (~c0_1(a183)) | c3_1(a133) | c1_1(a133) | c0_1(a133) | c2_1(a133) | c1_1(a133) | c0_1(a133)) <=> (c1_1(a183) | c2_1(a183) | c0_1(a133) | c1_1(a133) | c2_1(a133) | (~ndr1_0) | c3_1(a133) | (~c0_1(a183)))),
% 0.79/0.95 inference(rewrite,[status(thm)],[])).
% 0.79/0.95 tff(2154,plain,
% 0.79/0.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a183) | c2_1(a183) | (~c0_1(a183)) | c3_1(a133) | c1_1(a133) | c0_1(a133) | c2_1(a133) | c1_1(a133) | c0_1(a133))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a183) | c2_1(a183) | c0_1(a133) | c1_1(a133) | c2_1(a133) | (~ndr1_0) | c3_1(a133) | (~c0_1(a183))))),
% 0.79/0.95 inference(monotonicity,[status(thm)],[2153])).
% 0.79/0.95 tff(2155,plain,
% 0.79/0.95 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a183) | c2_1(a183) | (~c0_1(a183)) | c3_1(a133) | c1_1(a133) | c0_1(a133) | c2_1(a133) | c1_1(a133) | c0_1(a133))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a183) | c2_1(a183) | c0_1(a133) | c1_1(a133) | c2_1(a133) | (~ndr1_0) | c3_1(a133) | (~c0_1(a183)))),
% 0.79/0.95 inference(transitivity,[status(thm)],[2154, 2152])).
% 0.79/0.95 tff(2156,plain,
% 0.79/0.95 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a183) | c2_1(a183) | (~c0_1(a183)) | c3_1(a133) | c1_1(a133) | c0_1(a133) | c2_1(a133) | c1_1(a133) | c0_1(a133))),
% 0.79/0.95 inference(quant_inst,[status(thm)],[])).
% 0.79/0.95 tff(2157,plain,
% 0.79/0.95 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a183) | c2_1(a183) | c0_1(a133) | c1_1(a133) | c2_1(a133) | (~ndr1_0) | c3_1(a133) | (~c0_1(a183))),
% 0.79/0.96 inference(modus_ponens,[status(thm)],[2156, 2155])).
% 0.79/0.96 tff(2158,plain,
% 0.79/0.96 (~c0_1(a183)),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[2157, 175, 2151, 2145, 2122, 2096, 2095, 460, 2121])).
% 0.79/0.96 tff(2159,plain,
% 0.79/0.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a183) | c2_1(a183) | c2_1(a159) | c0_1(a133) | c1_1(a133) | (~ndr1_0) | c3_1(a133) | c1_1(a159) | (~c0_1(a159)) | c0_1(a183))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a183) | c2_1(a183) | c2_1(a159) | c0_1(a133) | c1_1(a133) | (~ndr1_0) | c3_1(a133) | c1_1(a159) | (~c0_1(a159)) | c0_1(a183))),
% 0.79/0.96 inference(rewrite,[status(thm)],[])).
% 0.79/0.96 tff(2160,plain,
% 0.79/0.96 (((~ndr1_0) | c1_1(a159) | c2_1(a159) | (~c0_1(a159)) | c3_1(a133) | c1_1(a133) | c0_1(a133) | c2_1(a183) | c1_1(a183) | c0_1(a183)) <=> (c1_1(a183) | c2_1(a183) | c2_1(a159) | c0_1(a133) | c1_1(a133) | (~ndr1_0) | c3_1(a133) | c1_1(a159) | (~c0_1(a159)) | c0_1(a183))),
% 0.79/0.96 inference(rewrite,[status(thm)],[])).
% 0.79/0.96 tff(2161,plain,
% 0.79/0.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a159) | c2_1(a159) | (~c0_1(a159)) | c3_1(a133) | c1_1(a133) | c0_1(a133) | c2_1(a183) | c1_1(a183) | c0_1(a183))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a183) | c2_1(a183) | c2_1(a159) | c0_1(a133) | c1_1(a133) | (~ndr1_0) | c3_1(a133) | c1_1(a159) | (~c0_1(a159)) | c0_1(a183)))),
% 0.79/0.96 inference(monotonicity,[status(thm)],[2160])).
% 0.79/0.96 tff(2162,plain,
% 0.79/0.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a159) | c2_1(a159) | (~c0_1(a159)) | c3_1(a133) | c1_1(a133) | c0_1(a133) | c2_1(a183) | c1_1(a183) | c0_1(a183))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a183) | c2_1(a183) | c2_1(a159) | c0_1(a133) | c1_1(a133) | (~ndr1_0) | c3_1(a133) | c1_1(a159) | (~c0_1(a159)) | c0_1(a183))),
% 0.79/0.96 inference(transitivity,[status(thm)],[2161, 2159])).
% 0.79/0.96 tff(2163,plain,
% 0.79/0.96 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a159) | c2_1(a159) | (~c0_1(a159)) | c3_1(a133) | c1_1(a133) | c0_1(a133) | c2_1(a183) | c1_1(a183) | c0_1(a183))),
% 0.79/0.96 inference(quant_inst,[status(thm)],[])).
% 0.79/0.96 tff(2164,plain,
% 0.79/0.96 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a183) | c2_1(a183) | c2_1(a159) | c0_1(a133) | c1_1(a133) | (~ndr1_0) | c3_1(a133) | c1_1(a159) | (~c0_1(a159)) | c0_1(a183)),
% 0.79/0.96 inference(modus_ponens,[status(thm)],[2163, 2162])).
% 0.79/0.96 tff(2165,plain,
% 0.79/0.96 ($false),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[2164, 175, 1821, 2151, 2145, 1813, 2122, 2096, 460, 2069, 2121, 2158])).
% 0.79/0.96 tff(2166,plain,(hskp4 | c0_1(a133) | c1_1(a133) | c1_1(a159) | c2_1(a133) | (~c2_1(a137)) | (~c3_1(a137)) | c0_1(a137)), inference(lemma,lemma(discharge,[]))).
% 0.79/0.96 tff(2167,plain,
% 0.79/0.96 (hskp4),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[2166, 2067, 2066, 1862, 2065, 2042, 2041, 2056])).
% 0.79/0.96 tff(2168,assumption,(hskp4), introduced(assumption)).
% 0.79/0.96 tff(2169,plain,
% 0.79/0.96 (((~hskp4) | (~c3_1(a130))) <=> ((~hskp4) | (~c3_1(a130)))),
% 0.79/0.96 inference(rewrite,[status(thm)],[])).
% 0.79/0.96 tff(2170,plain,
% 0.79/0.96 (((~c3_1(a130)) | (~hskp4)) <=> ((~hskp4) | (~c3_1(a130)))),
% 0.79/0.96 inference(rewrite,[status(thm)],[])).
% 0.79/0.96 tff(2171,axiom,((~c3_1(a130)) | (~hskp4)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause122')).
% 0.79/0.96 tff(2172,plain,
% 0.79/0.96 ((~hskp4) | (~c3_1(a130))),
% 0.79/0.96 inference(modus_ponens,[status(thm)],[2171, 2170])).
% 0.79/0.96 tff(2173,plain,
% 0.79/0.96 ((~hskp4) | (~c3_1(a130))),
% 0.79/0.96 inference(modus_ponens,[status(thm)],[2172, 2169])).
% 0.79/0.96 tff(2174,plain,
% 0.79/0.96 (~c3_1(a130)),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[2173, 2168])).
% 0.79/0.96 tff(2175,plain,
% 0.79/0.96 (((~hskp4) | c2_1(a130)) <=> ((~hskp4) | c2_1(a130))),
% 0.79/0.96 inference(rewrite,[status(thm)],[])).
% 0.79/0.96 tff(2176,axiom,((~hskp4) | c2_1(a130)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause78')).
% 0.79/0.96 tff(2177,plain,
% 0.79/0.96 ((~hskp4) | c2_1(a130)),
% 0.79/0.96 inference(modus_ponens,[status(thm)],[2176, 2175])).
% 0.79/0.96 tff(2178,plain,
% 0.79/0.96 ((~hskp4) | c2_1(a130)),
% 0.79/0.96 inference(modus_ponens,[status(thm)],[2177, 2175])).
% 0.79/0.96 tff(2179,plain,
% 0.79/0.96 ((~hskp4) | c2_1(a130)),
% 0.79/0.96 inference(modus_ponens,[status(thm)],[2178, 2175])).
% 0.79/0.96 tff(2180,plain,
% 0.79/0.96 ((~hskp4) | c2_1(a130)),
% 0.79/0.96 inference(modus_ponens,[status(thm)],[2179, 2175])).
% 0.79/0.96 tff(2181,plain,
% 0.79/0.96 ((~hskp4) | c2_1(a130)),
% 0.79/0.96 inference(modus_ponens,[status(thm)],[2180, 2175])).
% 0.79/0.96 tff(2182,plain,
% 0.79/0.96 (c2_1(a130)),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[2181, 2168])).
% 0.79/0.96 tff(2183,assumption,(c1_1(a137)), introduced(assumption)).
% 0.79/0.96 tff(2184,plain,
% 0.79/0.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c2_1(a159) | c3_1(a159) | c3_1(a130) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | c0_1(a130) | (~c2_1(a130)) | c1_1(a159))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c2_1(a159) | c3_1(a159) | c3_1(a130) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | c0_1(a130) | (~c2_1(a130)) | c1_1(a159))),
% 0.79/0.96 inference(rewrite,[status(thm)],[])).
% 0.79/0.96 tff(2185,plain,
% 0.79/0.96 (((~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | c3_1(a130) | c0_1(a130) | (~c2_1(a130)) | c2_1(a159) | c1_1(a159) | c3_1(a159)) <=> (c2_1(a159) | c3_1(a159) | c3_1(a130) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | c0_1(a130) | (~c2_1(a130)) | c1_1(a159))),
% 0.79/0.96 inference(rewrite,[status(thm)],[])).
% 0.79/0.96 tff(2186,plain,
% 0.79/0.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | c3_1(a130) | c0_1(a130) | (~c2_1(a130)) | c2_1(a159) | c1_1(a159) | c3_1(a159))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c2_1(a159) | c3_1(a159) | c3_1(a130) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | c0_1(a130) | (~c2_1(a130)) | c1_1(a159)))),
% 0.79/0.96 inference(monotonicity,[status(thm)],[2185])).
% 0.79/0.96 tff(2187,plain,
% 0.79/0.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | c3_1(a130) | c0_1(a130) | (~c2_1(a130)) | c2_1(a159) | c1_1(a159) | c3_1(a159))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c2_1(a159) | c3_1(a159) | c3_1(a130) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | c0_1(a130) | (~c2_1(a130)) | c1_1(a159))),
% 0.79/0.96 inference(transitivity,[status(thm)],[2186, 2184])).
% 0.79/0.96 tff(2188,plain,
% 0.79/0.96 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | c3_1(a130) | c0_1(a130) | (~c2_1(a130)) | c2_1(a159) | c1_1(a159) | c3_1(a159))),
% 0.79/0.96 inference(quant_inst,[status(thm)],[])).
% 0.79/0.96 tff(2189,plain,
% 0.79/0.96 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c2_1(a159) | c3_1(a159) | c3_1(a130) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | c0_1(a130) | (~c2_1(a130)) | c1_1(a159)),
% 0.79/0.96 inference(modus_ponens,[status(thm)],[2188, 2187])).
% 0.79/0.96 tff(2190,plain,
% 0.79/0.96 (c0_1(a130)),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[2189, 175, 2183, 2114, 2113, 2182, 1813, 1807, 2174, 1104, 2069])).
% 0.79/0.96 tff(2191,plain,
% 0.79/0.96 (((~hskp4) | c1_1(a130)) <=> ((~hskp4) | c1_1(a130))),
% 0.79/0.96 inference(rewrite,[status(thm)],[])).
% 0.79/0.96 tff(2192,axiom,((~hskp4) | c1_1(a130)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause77')).
% 0.79/0.96 tff(2193,plain,
% 0.79/0.96 ((~hskp4) | c1_1(a130)),
% 0.79/0.96 inference(modus_ponens,[status(thm)],[2192, 2191])).
% 0.79/0.96 tff(2194,plain,
% 0.79/0.96 ((~hskp4) | c1_1(a130)),
% 0.79/0.96 inference(modus_ponens,[status(thm)],[2193, 2191])).
% 0.79/0.96 tff(2195,plain,
% 0.79/0.96 ((~hskp4) | c1_1(a130)),
% 0.79/0.96 inference(modus_ponens,[status(thm)],[2194, 2191])).
% 0.79/0.96 tff(2196,plain,
% 0.79/0.96 ((~hskp4) | c1_1(a130)),
% 0.79/0.96 inference(modus_ponens,[status(thm)],[2195, 2191])).
% 0.79/0.96 tff(2197,plain,
% 0.79/0.96 ((~hskp4) | c1_1(a130)),
% 0.79/0.96 inference(modus_ponens,[status(thm)],[2196, 2191])).
% 0.79/0.96 tff(2198,plain,
% 0.79/0.96 (c1_1(a130)),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[2197, 2168])).
% 0.79/0.96 tff(2199,plain,
% 0.79/0.96 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp13 | c3_1(a130) | (~ndr1_0) | (~c1_1(a130)) | (~c0_1(a130)) | (~c2_1(a130)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp13 | c3_1(a130) | (~ndr1_0) | (~c1_1(a130)) | (~c0_1(a130)) | (~c2_1(a130)))),
% 0.79/0.96 inference(rewrite,[status(thm)],[])).
% 0.79/0.96 tff(2200,plain,
% 0.79/0.96 ((hskp13 | (~ndr1_0) | (~c2_1(a130)) | (~c1_1(a130)) | (~c0_1(a130)) | c3_1(a130) | (~c1_1(a130)) | (~c0_1(a130))) <=> (hskp13 | c3_1(a130) | (~ndr1_0) | (~c1_1(a130)) | (~c0_1(a130)) | (~c2_1(a130)))),
% 0.79/0.96 inference(rewrite,[status(thm)],[])).
% 0.79/0.96 tff(2201,plain,
% 0.79/0.96 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp13 | (~ndr1_0) | (~c2_1(a130)) | (~c1_1(a130)) | (~c0_1(a130)) | c3_1(a130) | (~c1_1(a130)) | (~c0_1(a130)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp13 | c3_1(a130) | (~ndr1_0) | (~c1_1(a130)) | (~c0_1(a130)) | (~c2_1(a130))))),
% 0.79/0.96 inference(monotonicity,[status(thm)],[2200])).
% 0.79/0.96 tff(2202,plain,
% 0.79/0.96 (((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp13 | (~ndr1_0) | (~c2_1(a130)) | (~c1_1(a130)) | (~c0_1(a130)) | c3_1(a130) | (~c1_1(a130)) | (~c0_1(a130)))) <=> ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp13 | c3_1(a130) | (~ndr1_0) | (~c1_1(a130)) | (~c0_1(a130)) | (~c2_1(a130)))),
% 0.79/0.96 inference(transitivity,[status(thm)],[2201, 2199])).
% 0.79/0.96 tff(2203,plain,
% 0.79/0.96 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | (hskp13 | (~ndr1_0) | (~c2_1(a130)) | (~c1_1(a130)) | (~c0_1(a130)) | c3_1(a130) | (~c1_1(a130)) | (~c0_1(a130)))),
% 0.79/0.96 inference(quant_inst,[status(thm)],[])).
% 0.79/0.96 tff(2204,plain,
% 0.79/0.96 ((~![V: $i, U: $i] : (hskp13 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c3_1(V) | (~c1_1(V)) | (~c0_1(V)))) | hskp13 | c3_1(a130) | (~ndr1_0) | (~c1_1(a130)) | (~c0_1(a130)) | (~c2_1(a130))),
% 0.79/0.96 inference(modus_ponens,[status(thm)],[2203, 2202])).
% 0.79/0.96 tff(2205,plain,
% 0.79/0.96 ($false),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[2204, 175, 11, 2198, 2182, 2174, 21, 2190])).
% 0.79/0.96 tff(2206,plain,((~hskp4) | hskp13 | (~c1_1(a137)) | (~c2_1(a137)) | (~c3_1(a137)) | c1_1(a159)), inference(lemma,lemma(discharge,[]))).
% 0.79/0.96 tff(2207,plain,
% 0.79/0.96 (hskp13),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[2206, 2167, 1862, 2042, 2041, 2057])).
% 0.79/0.96 tff(2208,plain,
% 0.79/0.96 (~c3_1(a144)),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[928, 2207])).
% 0.79/0.96 tff(2209,plain,
% 0.79/0.96 (~c0_1(a144)),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[949, 2207])).
% 0.79/0.96 tff(2210,plain,
% 0.79/0.96 (c2_1(a144)),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[936, 2207])).
% 0.79/0.96 tff(2211,plain,
% 0.79/0.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c2_1(a159) | c3_1(a159) | c0_1(a144) | c3_1(a144) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | (~c2_1(a144)) | c1_1(a159))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c2_1(a159) | c3_1(a159) | c0_1(a144) | c3_1(a144) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | (~c2_1(a144)) | c1_1(a159))),
% 0.79/0.96 inference(rewrite,[status(thm)],[])).
% 0.79/0.96 tff(2212,plain,
% 0.79/0.96 (((~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | c3_1(a144) | c0_1(a144) | (~c2_1(a144)) | c2_1(a159) | c1_1(a159) | c3_1(a159)) <=> (c2_1(a159) | c3_1(a159) | c0_1(a144) | c3_1(a144) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | (~c2_1(a144)) | c1_1(a159))),
% 0.79/0.96 inference(rewrite,[status(thm)],[])).
% 0.79/0.96 tff(2213,plain,
% 0.79/0.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | c3_1(a144) | c0_1(a144) | (~c2_1(a144)) | c2_1(a159) | c1_1(a159) | c3_1(a159))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c2_1(a159) | c3_1(a159) | c0_1(a144) | c3_1(a144) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | (~c2_1(a144)) | c1_1(a159)))),
% 0.79/0.96 inference(monotonicity,[status(thm)],[2212])).
% 0.79/0.96 tff(2214,plain,
% 0.79/0.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | c3_1(a144) | c0_1(a144) | (~c2_1(a144)) | c2_1(a159) | c1_1(a159) | c3_1(a159))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c2_1(a159) | c3_1(a159) | c0_1(a144) | c3_1(a144) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | (~c2_1(a144)) | c1_1(a159))),
% 0.79/0.96 inference(transitivity,[status(thm)],[2213, 2211])).
% 0.79/0.96 tff(2215,plain,
% 0.79/0.96 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | c3_1(a144) | c0_1(a144) | (~c2_1(a144)) | c2_1(a159) | c1_1(a159) | c3_1(a159))),
% 0.79/0.96 inference(quant_inst,[status(thm)],[])).
% 0.79/0.96 tff(2216,plain,
% 0.79/0.96 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c2_1(a159) | c3_1(a159) | c0_1(a144) | c3_1(a144) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | (~c2_1(a144)) | c1_1(a159)),
% 0.79/0.96 inference(modus_ponens,[status(thm)],[2215, 2214])).
% 0.79/0.96 tff(2217,plain,
% 0.79/0.96 (c1_1(a159)),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[2216, 175, 2183, 2114, 2113, 1503, 1813, 1807, 1502, 1501, 1104])).
% 0.79/0.96 tff(2218,assumption,(hskp11), introduced(assumption)).
% 0.79/0.96 tff(2219,plain,
% 0.79/0.96 (~c3_1(a139)),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[1407, 2218])).
% 0.79/0.96 tff(2220,plain,
% 0.79/0.96 (~c1_1(a139)),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[1413, 2218])).
% 0.79/0.96 tff(2221,plain,
% 0.79/0.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | (c2_1(a159) | c1_1(a139) | c3_1(a139) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | (~c2_1(a139)) | (~c1_1(a159)) | (~c0_1(a159)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | c2_1(a159) | c1_1(a139) | c3_1(a139) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | (~c2_1(a139)) | (~c1_1(a159)) | (~c0_1(a159)))),
% 0.79/0.96 inference(rewrite,[status(thm)],[])).
% 0.79/0.96 tff(2222,plain,
% 0.79/0.96 (((~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | c2_1(a159) | (~c1_1(a159)) | (~c0_1(a159)) | c1_1(a139) | c3_1(a139) | (~c2_1(a139))) <=> (c2_1(a159) | c1_1(a139) | c3_1(a139) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | (~c2_1(a139)) | (~c1_1(a159)) | (~c0_1(a159)))),
% 0.79/0.96 inference(rewrite,[status(thm)],[])).
% 0.79/0.96 tff(2223,plain,
% 0.79/0.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | c2_1(a159) | (~c1_1(a159)) | (~c0_1(a159)) | c1_1(a139) | c3_1(a139) | (~c2_1(a139)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | (c2_1(a159) | c1_1(a139) | c3_1(a139) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | (~c2_1(a139)) | (~c1_1(a159)) | (~c0_1(a159))))),
% 0.79/0.96 inference(monotonicity,[status(thm)],[2222])).
% 0.79/0.96 tff(2224,plain,
% 0.79/0.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | c2_1(a159) | (~c1_1(a159)) | (~c0_1(a159)) | c1_1(a139) | c3_1(a139) | (~c2_1(a139)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | c2_1(a159) | c1_1(a139) | c3_1(a139) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | (~c2_1(a139)) | (~c1_1(a159)) | (~c0_1(a159)))),
% 0.79/0.96 inference(transitivity,[status(thm)],[2223, 2221])).
% 0.79/0.96 tff(2225,plain,
% 0.79/0.96 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | c2_1(a159) | (~c1_1(a159)) | (~c0_1(a159)) | c1_1(a139) | c3_1(a139) | (~c2_1(a139)))),
% 0.79/0.96 inference(quant_inst,[status(thm)],[])).
% 0.79/0.96 tff(2226,plain,
% 0.79/0.96 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | c2_1(a159) | c1_1(a139) | c3_1(a139) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | (~c2_1(a139)) | (~c1_1(a159)) | (~c0_1(a159))),
% 0.79/0.96 inference(modus_ponens,[status(thm)],[2225, 2224])).
% 0.79/0.96 tff(2227,plain,
% 0.79/0.96 (~c2_1(a139)),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[2226, 175, 2183, 2114, 2113, 1821, 1813, 2220, 2219, 94, 2217])).
% 0.79/0.96 tff(2228,plain,
% 0.79/0.96 ($false),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[1799, 175, 2183, 2114, 2113, 1503, 1502, 1501, 2220, 2219, 1104, 2227])).
% 0.79/0.96 tff(2229,plain,((~hskp11) | (~c1_1(a137)) | (~c2_1(a137)) | (~c3_1(a137)) | (~c2_1(a144)) | c0_1(a144) | c3_1(a144)), inference(lemma,lemma(discharge,[]))).
% 0.79/0.96 tff(2230,plain,
% 0.79/0.96 (~hskp11),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[2229, 2210, 2042, 2041, 2057, 2209, 2208])).
% 0.79/0.96 tff(2231,plain,
% 0.79/0.96 (hskp11 | hskp10 | (~c1_1(a128))),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[1635, 175, 2005, 2004, 1379])).
% 0.79/0.96 tff(2232,plain,
% 0.79/0.96 (hskp10),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[2231, 2230, 2022])).
% 0.79/0.96 tff(2233,plain,
% 0.79/0.96 (~c1_1(a138)),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[101, 2232])).
% 0.79/0.96 tff(2234,plain,
% 0.79/0.96 (c3_1(a138)),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[109, 2232])).
% 0.79/0.96 tff(2235,plain,
% 0.79/0.96 (c0_1(a138)),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[117, 2232])).
% 0.79/0.96 tff(2236,plain,
% 0.79/0.96 ($false),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[355, 175, 2235, 2234, 2233, 2067, 2066, 2065, 2005, 2004, 2003, 258])).
% 0.79/0.96 tff(2237,plain,(hskp15), inference(lemma,lemma(discharge,[]))).
% 0.79/0.96 tff(2238,plain,
% 0.79/0.96 (~c1_1(a149)),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[531, 2237])).
% 0.79/0.96 tff(2239,plain,
% 0.79/0.96 (~c2_1(a149)),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[525, 2237])).
% 0.79/0.96 tff(2240,assumption,(~c3_1(a149)), introduced(assumption)).
% 0.79/0.96 tff(2241,plain,
% 0.79/0.96 (~hskp15),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[246, 2240])).
% 0.79/0.96 tff(2242,plain,
% 0.79/0.96 (~c1_1(a159)),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[1861, 2241])).
% 0.79/0.96 tff(2243,plain,
% 0.79/0.96 (c1_1(a128)),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[2021, 175, 1821, 1813, 2005, 2004, 2003, 460, 2242])).
% 0.79/0.96 tff(2244,plain,
% 0.79/0.96 (hskp27),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[2039, 2243, 2241])).
% 0.79/0.96 tff(2245,plain,
% 0.79/0.96 (c3_1(a137)),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[1146, 2244])).
% 0.79/0.96 tff(2246,plain,
% 0.79/0.96 (c2_1(a137)),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[1154, 2244])).
% 0.79/0.96 tff(2247,plain,
% 0.79/0.96 (c1_1(a137)),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[1162, 2244])).
% 0.79/0.96 tff(2248,plain,
% 0.79/0.96 (~hskp16),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[2048, 2241])).
% 0.79/0.96 tff(2249,plain,
% 0.79/0.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c3_1(a149) | c2_1(a159) | c1_1(a149) | c2_1(a149) | (~ndr1_0) | c0_1(a149) | c1_1(a159) | (~c0_1(a159)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c3_1(a149) | c2_1(a159) | c1_1(a149) | c2_1(a149) | (~ndr1_0) | c0_1(a149) | c1_1(a159) | (~c0_1(a159)))),
% 0.79/0.96 inference(rewrite,[status(thm)],[])).
% 0.79/0.96 tff(2250,plain,
% 0.79/0.96 (((~ndr1_0) | c1_1(a159) | c2_1(a159) | (~c0_1(a159)) | c3_1(a149) | c1_1(a149) | c0_1(a149) | c2_1(a149) | c1_1(a149) | c0_1(a149)) <=> (c3_1(a149) | c2_1(a159) | c1_1(a149) | c2_1(a149) | (~ndr1_0) | c0_1(a149) | c1_1(a159) | (~c0_1(a159)))),
% 0.79/0.96 inference(rewrite,[status(thm)],[])).
% 0.79/0.96 tff(2251,plain,
% 0.79/0.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a159) | c2_1(a159) | (~c0_1(a159)) | c3_1(a149) | c1_1(a149) | c0_1(a149) | c2_1(a149) | c1_1(a149) | c0_1(a149))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c3_1(a149) | c2_1(a159) | c1_1(a149) | c2_1(a149) | (~ndr1_0) | c0_1(a149) | c1_1(a159) | (~c0_1(a159))))),
% 0.79/0.96 inference(monotonicity,[status(thm)],[2250])).
% 0.79/0.96 tff(2252,plain,
% 0.79/0.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a159) | c2_1(a159) | (~c0_1(a159)) | c3_1(a149) | c1_1(a149) | c0_1(a149) | c2_1(a149) | c1_1(a149) | c0_1(a149))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c3_1(a149) | c2_1(a159) | c1_1(a149) | c2_1(a149) | (~ndr1_0) | c0_1(a149) | c1_1(a159) | (~c0_1(a159)))),
% 0.79/0.96 inference(transitivity,[status(thm)],[2251, 2249])).
% 0.79/0.96 tff(2253,plain,
% 0.79/0.96 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a159) | c2_1(a159) | (~c0_1(a159)) | c3_1(a149) | c1_1(a149) | c0_1(a149) | c2_1(a149) | c1_1(a149) | c0_1(a149))),
% 0.79/0.96 inference(quant_inst,[status(thm)],[])).
% 0.79/0.96 tff(2254,plain,
% 0.79/0.96 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c3_1(a149) | c2_1(a159) | c1_1(a149) | c2_1(a149) | (~ndr1_0) | c0_1(a149) | c1_1(a159) | (~c0_1(a159))),
% 0.79/0.96 inference(modus_ponens,[status(thm)],[2253, 2252])).
% 0.79/0.96 tff(2255,plain,
% 0.79/0.96 (c0_1(a149)),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[2254, 175, 1821, 2240, 1813, 596, 595, 460, 2242])).
% 0.79/0.96 tff(2256,plain,
% 0.79/0.96 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp16 | c1_1(a149) | c2_1(a149) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c0_1(a137)) | (~c0_1(a149)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp16 | c1_1(a149) | c2_1(a149) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c0_1(a137)) | (~c0_1(a149)))),
% 0.79/0.96 inference(rewrite,[status(thm)],[])).
% 0.79/0.96 tff(2257,plain,
% 0.79/0.96 ((hskp16 | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c0_1(a137)) | c1_1(a149) | c2_1(a149) | (~c0_1(a149))) <=> (hskp16 | c1_1(a149) | c2_1(a149) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c0_1(a137)) | (~c0_1(a149)))),
% 0.79/0.96 inference(rewrite,[status(thm)],[])).
% 0.79/0.96 tff(2258,plain,
% 0.79/0.96 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp16 | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c0_1(a137)) | c1_1(a149) | c2_1(a149) | (~c0_1(a149)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp16 | c1_1(a149) | c2_1(a149) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c0_1(a137)) | (~c0_1(a149))))),
% 0.79/0.96 inference(monotonicity,[status(thm)],[2257])).
% 0.79/0.96 tff(2259,plain,
% 0.79/0.96 (((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp16 | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c0_1(a137)) | c1_1(a149) | c2_1(a149) | (~c0_1(a149)))) <=> ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp16 | c1_1(a149) | c2_1(a149) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c0_1(a137)) | (~c0_1(a149)))),
% 0.79/0.96 inference(transitivity,[status(thm)],[2258, 2256])).
% 0.79/0.96 tff(2260,plain,
% 0.79/0.96 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | (hskp16 | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c0_1(a137)) | c1_1(a149) | c2_1(a149) | (~c0_1(a149)))),
% 0.79/0.96 inference(quant_inst,[status(thm)],[])).
% 0.79/0.96 tff(2261,plain,
% 0.79/0.96 ((~![V: $i, U: $i] : (hskp16 | (~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c0_1(U)) | c1_1(V) | c2_1(V) | (~c0_1(V)))) | hskp16 | c1_1(a149) | c2_1(a149) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c0_1(a137)) | (~c0_1(a149))),
% 0.79/0.96 inference(modus_ponens,[status(thm)],[2260, 2259])).
% 0.79/0.96 tff(2262,plain,
% 0.79/0.96 (hskp16 | (~c0_1(a137))),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[2261, 175, 2246, 2245, 596, 595, 2015, 2255])).
% 0.79/0.96 tff(2263,plain,
% 0.79/0.96 (~c0_1(a137)),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[2262, 2248])).
% 0.79/0.96 tff(2264,plain,
% 0.79/0.96 (hskp6),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[2063, 175, 2247, 2245, 2005, 2003, 315, 2243, 2263])).
% 0.79/0.96 tff(2265,plain,
% 0.79/0.96 (~c2_1(a133)),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[336, 2264])).
% 0.79/0.96 tff(2266,plain,
% 0.79/0.96 (~c1_1(a133)),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[342, 2264])).
% 0.79/0.96 tff(2267,plain,
% 0.79/0.96 (~c0_1(a133)),
% 0.79/0.96 inference(unit_resolution,[status(thm)],[348, 2264])).
% 0.79/0.96 tff(2268,plain,
% 0.79/0.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a183) | c2_1(a183) | c1_1(a149) | c2_1(a149) | c0_1(a133) | c1_1(a133) | (~ndr1_0) | c3_1(a133) | (~c0_1(a149)) | c0_1(a183))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a183) | c2_1(a183) | c1_1(a149) | c2_1(a149) | c0_1(a133) | c1_1(a133) | (~ndr1_0) | c3_1(a133) | (~c0_1(a149)) | c0_1(a183))),
% 0.79/0.96 inference(rewrite,[status(thm)],[])).
% 0.79/0.96 tff(2269,plain,
% 0.79/0.96 (((~ndr1_0) | c1_1(a149) | c2_1(a149) | (~c0_1(a149)) | c3_1(a133) | c1_1(a133) | c0_1(a133) | c2_1(a183) | c1_1(a183) | c0_1(a183)) <=> (c1_1(a183) | c2_1(a183) | c1_1(a149) | c2_1(a149) | c0_1(a133) | c1_1(a133) | (~ndr1_0) | c3_1(a133) | (~c0_1(a149)) | c0_1(a183))),
% 0.79/0.96 inference(rewrite,[status(thm)],[])).
% 0.79/0.96 tff(2270,plain,
% 0.79/0.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a149) | c2_1(a149) | (~c0_1(a149)) | c3_1(a133) | c1_1(a133) | c0_1(a133) | c2_1(a183) | c1_1(a183) | c0_1(a183))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a183) | c2_1(a183) | c1_1(a149) | c2_1(a149) | c0_1(a133) | c1_1(a133) | (~ndr1_0) | c3_1(a133) | (~c0_1(a149)) | c0_1(a183)))),
% 0.79/0.96 inference(monotonicity,[status(thm)],[2269])).
% 0.79/0.96 tff(2271,plain,
% 0.79/0.96 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a149) | c2_1(a149) | (~c0_1(a149)) | c3_1(a133) | c1_1(a133) | c0_1(a133) | c2_1(a183) | c1_1(a183) | c0_1(a183))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a183) | c2_1(a183) | c1_1(a149) | c2_1(a149) | c0_1(a133) | c1_1(a133) | (~ndr1_0) | c3_1(a133) | (~c0_1(a149)) | c0_1(a183))),
% 0.79/0.97 inference(transitivity,[status(thm)],[2270, 2268])).
% 0.79/0.97 tff(2272,plain,
% 0.79/0.97 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a149) | c2_1(a149) | (~c0_1(a149)) | c3_1(a133) | c1_1(a133) | c0_1(a133) | c2_1(a183) | c1_1(a183) | c0_1(a183))),
% 0.79/0.97 inference(quant_inst,[status(thm)],[])).
% 0.79/0.97 tff(2273,plain,
% 0.79/0.97 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a183) | c2_1(a183) | c1_1(a149) | c2_1(a149) | c0_1(a133) | c1_1(a133) | (~ndr1_0) | c3_1(a133) | (~c0_1(a149)) | c0_1(a183)),
% 0.79/0.97 inference(modus_ponens,[status(thm)],[2272, 2271])).
% 0.79/0.97 tff(2274,plain,
% 0.79/0.97 ($false),
% 0.79/0.97 inference(unit_resolution,[status(thm)],[2273, 175, 2151, 2145, 596, 595, 2122, 2096, 460, 732, 2121, 2158])).
% 0.79/0.97 tff(2275,plain,(hskp4 | c1_1(a149) | c2_1(a149) | c0_1(a133) | c1_1(a133) | (~c0_1(a149)) | c2_1(a133) | (~c2_1(a137)) | (~c3_1(a137)) | c0_1(a137) | c1_1(a159)), inference(lemma,lemma(discharge,[]))).
% 0.79/0.97 tff(2276,plain,
% 0.79/0.97 (hskp4),
% 0.79/0.97 inference(unit_resolution,[status(thm)],[2275, 2267, 595, 596, 2266, 2255, 2265, 2246, 2245, 2263, 2242])).
% 0.79/0.97 tff(2277,plain,
% 0.79/0.97 (hskp13),
% 0.79/0.97 inference(unit_resolution,[status(thm)],[2206, 2276, 2247, 2246, 2245, 2242])).
% 0.79/0.97 tff(2278,plain,
% 0.79/0.97 (~c3_1(a144)),
% 0.79/0.97 inference(unit_resolution,[status(thm)],[928, 2277])).
% 0.79/0.97 tff(2279,plain,
% 0.79/0.97 (~c0_1(a144)),
% 0.79/0.97 inference(unit_resolution,[status(thm)],[949, 2277])).
% 0.79/0.97 tff(2280,plain,
% 0.79/0.97 (c2_1(a144)),
% 0.79/0.97 inference(unit_resolution,[status(thm)],[936, 2277])).
% 0.79/0.97 tff(2281,plain,
% 0.79/0.97 ($false),
% 0.79/0.97 inference(unit_resolution,[status(thm)],[2216, 175, 2247, 2246, 2245, 2280, 1813, 1807, 2279, 2278, 1104, 2242])).
% 0.79/0.97 tff(2282,plain,(c3_1(a149) | c2_1(a149) | c1_1(a149)), inference(lemma,lemma(discharge,[]))).
% 0.79/0.97 tff(2283,plain,
% 0.79/0.97 (c3_1(a149)),
% 0.79/0.97 inference(unit_resolution,[status(thm)],[2282, 596, 595])).
% 0.79/0.97 tff(2284,plain,
% 0.79/0.97 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | c2_1(a149) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c3_1(a149)) | c0_1(a149))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp9 | c2_1(a149) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c3_1(a149)) | c0_1(a149))),
% 0.79/0.97 inference(rewrite,[status(thm)],[])).
% 0.79/0.97 tff(2285,plain,
% 0.79/0.97 ((hskp9 | (~ndr1_0) | c0_1(a149) | c2_1(a149) | (~c3_1(a149)) | c3_1(a128) | c0_1(a128) | c2_1(a128)) <=> (hskp9 | c2_1(a149) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c3_1(a149)) | c0_1(a149))),
% 0.79/0.97 inference(rewrite,[status(thm)],[])).
% 0.79/0.97 tff(2286,plain,
% 0.79/0.97 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | (~ndr1_0) | c0_1(a149) | c2_1(a149) | (~c3_1(a149)) | c3_1(a128) | c0_1(a128) | c2_1(a128))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | c2_1(a149) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c3_1(a149)) | c0_1(a149)))),
% 0.79/0.97 inference(monotonicity,[status(thm)],[2285])).
% 0.79/0.97 tff(2287,plain,
% 0.79/0.97 (((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | (~ndr1_0) | c0_1(a149) | c2_1(a149) | (~c3_1(a149)) | c3_1(a128) | c0_1(a128) | c2_1(a128))) <=> ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp9 | c2_1(a149) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c3_1(a149)) | c0_1(a149))),
% 0.79/0.97 inference(transitivity,[status(thm)],[2286, 2284])).
% 0.79/0.97 tff(2288,plain,
% 0.79/0.97 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp9 | (~ndr1_0) | c0_1(a149) | c2_1(a149) | (~c3_1(a149)) | c3_1(a128) | c0_1(a128) | c2_1(a128))),
% 0.79/0.97 inference(quant_inst,[status(thm)],[])).
% 0.79/0.97 tff(2289,plain,
% 0.79/0.97 ((~![V: $i, U: $i] : (hskp9 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp9 | c2_1(a149) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c3_1(a149)) | c0_1(a149)),
% 0.79/0.97 inference(modus_ponens,[status(thm)],[2288, 2287])).
% 0.79/0.97 tff(2290,plain,
% 0.79/0.97 (hskp9),
% 0.79/0.97 inference(unit_resolution,[status(thm)],[2289, 175, 2283, 595, 2005, 2004, 2003, 31, 1304])).
% 0.79/0.97 tff(2291,plain,
% 0.79/0.97 (~c3_1(a136)),
% 0.79/0.97 inference(unit_resolution,[status(thm)],[759, 2290])).
% 0.79/0.97 tff(2292,plain,
% 0.79/0.97 (c2_1(a136)),
% 0.79/0.97 inference(unit_resolution,[status(thm)],[767, 2290])).
% 0.79/0.97 tff(2293,plain,
% 0.79/0.97 (c0_1(a136)),
% 0.79/0.97 inference(unit_resolution,[status(thm)],[783, 2290])).
% 0.79/0.97 tff(2294,plain,
% 0.79/0.97 (~c1_1(a136)),
% 0.79/0.97 inference(unit_resolution,[status(thm)],[1337, 175, 11, 2293, 2292, 2291, 21])).
% 0.79/0.97 tff(2295,plain,
% 0.79/0.97 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp27 | c2_1(a149) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c3_1(a149)) | c0_1(a149))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp27 | c2_1(a149) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c3_1(a149)) | c0_1(a149))),
% 0.79/0.97 inference(rewrite,[status(thm)],[])).
% 0.79/0.97 tff(2296,plain,
% 0.79/0.97 ((hskp27 | (~ndr1_0) | c0_1(a149) | c2_1(a149) | (~c3_1(a149)) | c3_1(a128) | c0_1(a128) | c2_1(a128)) <=> (hskp27 | c2_1(a149) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c3_1(a149)) | c0_1(a149))),
% 0.79/0.97 inference(rewrite,[status(thm)],[])).
% 0.79/0.97 tff(2297,plain,
% 0.79/0.97 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp27 | (~ndr1_0) | c0_1(a149) | c2_1(a149) | (~c3_1(a149)) | c3_1(a128) | c0_1(a128) | c2_1(a128))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp27 | c2_1(a149) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c3_1(a149)) | c0_1(a149)))),
% 0.79/0.97 inference(monotonicity,[status(thm)],[2296])).
% 0.79/0.97 tff(2298,plain,
% 0.79/0.97 (((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp27 | (~ndr1_0) | c0_1(a149) | c2_1(a149) | (~c3_1(a149)) | c3_1(a128) | c0_1(a128) | c2_1(a128))) <=> ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp27 | c2_1(a149) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c3_1(a149)) | c0_1(a149))),
% 0.79/0.97 inference(transitivity,[status(thm)],[2297, 2295])).
% 0.79/0.97 tff(2299,plain,
% 0.79/0.97 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | (hskp27 | (~ndr1_0) | c0_1(a149) | c2_1(a149) | (~c3_1(a149)) | c3_1(a128) | c0_1(a128) | c2_1(a128))),
% 0.79/0.97 inference(quant_inst,[status(thm)],[])).
% 0.79/0.97 tff(2300,plain,
% 0.79/0.97 ((~![V: $i, U: $i] : (hskp27 | (~ndr1_0) | c0_1(U) | c2_1(U) | (~c3_1(U)) | c3_1(V) | c0_1(V) | c2_1(V))) | hskp27 | c2_1(a149) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c3_1(a149)) | c0_1(a149)),
% 0.79/0.97 inference(modus_ponens,[status(thm)],[2299, 2298])).
% 0.79/0.97 tff(2301,plain,
% 0.79/0.97 (hskp27),
% 0.79/0.97 inference(unit_resolution,[status(thm)],[2300, 175, 2283, 595, 2005, 2004, 2003, 1131, 1304])).
% 0.79/0.97 tff(2302,plain,
% 0.79/0.97 (c3_1(a137)),
% 0.79/0.97 inference(unit_resolution,[status(thm)],[1146, 2301])).
% 0.79/0.97 tff(2303,plain,
% 0.79/0.97 (c2_1(a137)),
% 0.79/0.97 inference(unit_resolution,[status(thm)],[1154, 2301])).
% 0.79/0.97 tff(2304,plain,
% 0.79/0.97 (c1_1(a137)),
% 0.79/0.97 inference(unit_resolution,[status(thm)],[1162, 2301])).
% 0.79/0.97 tff(2305,plain,
% 0.79/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | (c2_1(a159) | c3_1(a136) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | c1_1(a136) | (~c2_1(a136)) | (~c1_1(a159)) | (~c0_1(a159)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | c2_1(a159) | c3_1(a136) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | c1_1(a136) | (~c2_1(a136)) | (~c1_1(a159)) | (~c0_1(a159)))),
% 0.79/0.97 inference(rewrite,[status(thm)],[])).
% 0.79/0.97 tff(2306,plain,
% 0.79/0.97 (((~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | c2_1(a159) | (~c1_1(a159)) | (~c0_1(a159)) | c1_1(a136) | c3_1(a136) | (~c2_1(a136))) <=> (c2_1(a159) | c3_1(a136) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | c1_1(a136) | (~c2_1(a136)) | (~c1_1(a159)) | (~c0_1(a159)))),
% 0.79/0.97 inference(rewrite,[status(thm)],[])).
% 0.79/0.97 tff(2307,plain,
% 0.79/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | c2_1(a159) | (~c1_1(a159)) | (~c0_1(a159)) | c1_1(a136) | c3_1(a136) | (~c2_1(a136)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | (c2_1(a159) | c3_1(a136) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | c1_1(a136) | (~c2_1(a136)) | (~c1_1(a159)) | (~c0_1(a159))))),
% 0.79/0.97 inference(monotonicity,[status(thm)],[2306])).
% 0.79/0.97 tff(2308,plain,
% 0.79/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | c2_1(a159) | (~c1_1(a159)) | (~c0_1(a159)) | c1_1(a136) | c3_1(a136) | (~c2_1(a136)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | c2_1(a159) | c3_1(a136) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | c1_1(a136) | (~c2_1(a136)) | (~c1_1(a159)) | (~c0_1(a159)))),
% 0.79/0.97 inference(transitivity,[status(thm)],[2307, 2305])).
% 0.79/0.97 tff(2309,plain,
% 0.79/0.97 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | c2_1(a159) | (~c1_1(a159)) | (~c0_1(a159)) | c1_1(a136) | c3_1(a136) | (~c2_1(a136)))),
% 0.79/0.97 inference(quant_inst,[status(thm)],[])).
% 0.79/0.97 tff(2310,plain,
% 0.79/0.97 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c2_1(V) | (~c1_1(V)) | (~c0_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | c2_1(a159) | c3_1(a136) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | c1_1(a136) | (~c2_1(a136)) | (~c1_1(a159)) | (~c0_1(a159))),
% 0.79/0.97 inference(modus_ponens,[status(thm)],[2309, 2308])).
% 0.79/0.97 tff(2311,plain,
% 0.79/0.97 (~c1_1(a159)),
% 0.79/0.97 inference(unit_resolution,[status(thm)],[2310, 175, 2304, 2303, 2302, 1821, 2292, 1813, 2291, 94, 2294])).
% 0.79/0.97 tff(2312,plain,
% 0.79/0.97 (~hskp4),
% 0.79/0.97 inference(unit_resolution,[status(thm)],[2206, 2311, 11, 2303, 2302, 2304])).
% 0.79/0.97 tff(2313,plain,
% 0.79/0.97 (hskp5),
% 0.79/0.97 inference(unit_resolution,[status(thm)],[2087, 2312, 2311])).
% 0.79/0.97 tff(2314,assumption,(hskp5), introduced(assumption)).
% 0.79/0.97 tff(2315,plain,
% 0.79/0.97 (~c2_1(a131)),
% 0.79/0.97 inference(unit_resolution,[status(thm)],[2093, 2314])).
% 0.79/0.97 tff(2316,plain,
% 0.79/0.97 (c3_1(a131)),
% 0.79/0.97 inference(unit_resolution,[status(thm)],[2103, 2314])).
% 0.79/0.97 tff(2317,plain,
% 0.79/0.97 (c1_1(a131)),
% 0.79/0.97 inference(unit_resolution,[status(thm)],[2111, 2314])).
% 0.79/0.97 tff(2318,plain,
% 0.79/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | (c3_1(a136) | c2_1(a131) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c3_1(a131)) | (~c1_1(a131)) | (~c1_1(a128)) | c1_1(a136) | (~c2_1(a136)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | c3_1(a136) | c2_1(a131) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c3_1(a131)) | (~c1_1(a131)) | (~c1_1(a128)) | c1_1(a136) | (~c2_1(a136)))),
% 0.79/0.97 inference(rewrite,[status(thm)],[])).
% 0.79/0.97 tff(2319,plain,
% 0.79/0.97 (((~ndr1_0) | c2_1(a131) | (~c3_1(a131)) | (~c1_1(a131)) | c3_1(a128) | c2_1(a128) | (~c1_1(a128)) | c1_1(a136) | c3_1(a136) | (~c2_1(a136))) <=> (c3_1(a136) | c2_1(a131) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c3_1(a131)) | (~c1_1(a131)) | (~c1_1(a128)) | c1_1(a136) | (~c2_1(a136)))),
% 0.79/0.97 inference(rewrite,[status(thm)],[])).
% 0.79/0.97 tff(2320,plain,
% 0.79/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a131) | (~c3_1(a131)) | (~c1_1(a131)) | c3_1(a128) | c2_1(a128) | (~c1_1(a128)) | c1_1(a136) | c3_1(a136) | (~c2_1(a136)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | (c3_1(a136) | c2_1(a131) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c3_1(a131)) | (~c1_1(a131)) | (~c1_1(a128)) | c1_1(a136) | (~c2_1(a136))))),
% 0.79/0.97 inference(monotonicity,[status(thm)],[2319])).
% 0.79/0.97 tff(2321,plain,
% 0.79/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a131) | (~c3_1(a131)) | (~c1_1(a131)) | c3_1(a128) | c2_1(a128) | (~c1_1(a128)) | c1_1(a136) | c3_1(a136) | (~c2_1(a136)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | c3_1(a136) | c2_1(a131) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c3_1(a131)) | (~c1_1(a131)) | (~c1_1(a128)) | c1_1(a136) | (~c2_1(a136)))),
% 0.79/0.97 inference(transitivity,[status(thm)],[2320, 2318])).
% 0.79/0.97 tff(2322,plain,
% 0.79/0.97 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a131) | (~c3_1(a131)) | (~c1_1(a131)) | c3_1(a128) | c2_1(a128) | (~c1_1(a128)) | c1_1(a136) | c3_1(a136) | (~c2_1(a136)))),
% 0.79/0.97 inference(quant_inst,[status(thm)],[])).
% 0.79/0.97 tff(2323,plain,
% 0.79/0.97 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | c3_1(a136) | c2_1(a131) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c3_1(a131)) | (~c1_1(a131)) | (~c1_1(a128)) | c1_1(a136) | (~c2_1(a136))),
% 0.79/0.97 inference(modus_ponens,[status(thm)],[2322, 2321])).
% 0.79/0.97 tff(2324,plain,
% 0.79/0.97 ($false),
% 0.79/0.97 inference(unit_resolution,[status(thm)],[2323, 175, 1053, 2317, 2316, 1065, 2315, 2004, 2003, 10, 625, 1052])).
% 0.79/0.97 tff(2325,plain,((~hskp5) | (~c2_1(a136)) | c3_1(a136) | (~c1_1(a128)) | c1_1(a136)), inference(lemma,lemma(discharge,[]))).
% 0.79/0.97 tff(2326,plain,
% 0.79/0.97 (~c1_1(a128)),
% 0.79/0.97 inference(unit_resolution,[status(thm)],[2325, 2313, 2291, 2294, 2292])).
% 0.79/0.97 tff(2327,plain,
% 0.79/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a159) | c1_1(a149) | c2_1(a149) | c0_1(a128) | c3_1(a128) | (~ndr1_0) | c1_1(a128) | c0_1(a149) | c1_1(a159) | (~c0_1(a159)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a159) | c1_1(a149) | c2_1(a149) | c0_1(a128) | c3_1(a128) | (~ndr1_0) | c1_1(a128) | c0_1(a149) | c1_1(a159) | (~c0_1(a159)))),
% 0.79/0.97 inference(rewrite,[status(thm)],[])).
% 0.79/0.97 tff(2328,plain,
% 0.79/0.97 (((~ndr1_0) | c1_1(a159) | c2_1(a159) | (~c0_1(a159)) | c3_1(a128) | c1_1(a128) | c0_1(a128) | c2_1(a149) | c1_1(a149) | c0_1(a149)) <=> (c2_1(a159) | c1_1(a149) | c2_1(a149) | c0_1(a128) | c3_1(a128) | (~ndr1_0) | c1_1(a128) | c0_1(a149) | c1_1(a159) | (~c0_1(a159)))),
% 0.79/0.97 inference(rewrite,[status(thm)],[])).
% 0.79/0.97 tff(2329,plain,
% 0.79/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a159) | c2_1(a159) | (~c0_1(a159)) | c3_1(a128) | c1_1(a128) | c0_1(a128) | c2_1(a149) | c1_1(a149) | c0_1(a149))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c2_1(a159) | c1_1(a149) | c2_1(a149) | c0_1(a128) | c3_1(a128) | (~ndr1_0) | c1_1(a128) | c0_1(a149) | c1_1(a159) | (~c0_1(a159))))),
% 0.79/0.97 inference(monotonicity,[status(thm)],[2328])).
% 0.79/0.97 tff(2330,plain,
% 0.79/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a159) | c2_1(a159) | (~c0_1(a159)) | c3_1(a128) | c1_1(a128) | c0_1(a128) | c2_1(a149) | c1_1(a149) | c0_1(a149))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a159) | c1_1(a149) | c2_1(a149) | c0_1(a128) | c3_1(a128) | (~ndr1_0) | c1_1(a128) | c0_1(a149) | c1_1(a159) | (~c0_1(a159)))),
% 0.79/0.97 inference(transitivity,[status(thm)],[2329, 2327])).
% 0.79/0.97 tff(2331,plain,
% 0.79/0.97 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a159) | c2_1(a159) | (~c0_1(a159)) | c3_1(a128) | c1_1(a128) | c0_1(a128) | c2_1(a149) | c1_1(a149) | c0_1(a149))),
% 0.79/0.97 inference(quant_inst,[status(thm)],[])).
% 0.79/0.97 tff(2332,plain,
% 0.79/0.97 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c2_1(a159) | c1_1(a149) | c2_1(a149) | c0_1(a128) | c3_1(a128) | (~ndr1_0) | c1_1(a128) | c0_1(a149) | c1_1(a159) | (~c0_1(a159))),
% 0.79/0.97 inference(modus_ponens,[status(thm)],[2331, 2330])).
% 0.79/0.97 tff(2333,plain,
% 0.79/0.97 ($false),
% 0.79/0.97 inference(unit_resolution,[status(thm)],[2332, 175, 1821, 1813, 596, 595, 2005, 2003, 460, 2326, 1304, 2311])).
% 0.79/0.97 tff(2334,plain,(c0_1(a149) | c1_1(a149) | c2_1(a149) | hskp13), inference(lemma,lemma(discharge,[]))).
% 0.79/0.97 tff(2335,plain,
% 0.79/0.97 (c0_1(a149)),
% 0.79/0.97 inference(unit_resolution,[status(thm)],[2334, 11, 595, 596])).
% 0.79/0.97 tff(2336,plain,
% 0.79/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a149) | c2_1(a149) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | c1_1(a128) | (~c0_1(a149)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a149) | c2_1(a149) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | c1_1(a128) | (~c0_1(a149)))),
% 0.79/0.97 inference(rewrite,[status(thm)],[])).
% 0.79/0.97 tff(2337,plain,
% 0.79/0.97 (((~ndr1_0) | c1_1(a149) | c2_1(a149) | (~c0_1(a149)) | c3_1(a128) | c1_1(a128) | c0_1(a128) | c2_1(a128) | c1_1(a128) | c0_1(a128)) <=> (c1_1(a149) | c2_1(a149) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | c1_1(a128) | (~c0_1(a149)))),
% 0.79/0.97 inference(rewrite,[status(thm)],[])).
% 0.79/0.97 tff(2338,plain,
% 0.79/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a149) | c2_1(a149) | (~c0_1(a149)) | c3_1(a128) | c1_1(a128) | c0_1(a128) | c2_1(a128) | c1_1(a128) | c0_1(a128))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a149) | c2_1(a149) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | c1_1(a128) | (~c0_1(a149))))),
% 0.79/0.97 inference(monotonicity,[status(thm)],[2337])).
% 0.79/0.97 tff(2339,plain,
% 0.79/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a149) | c2_1(a149) | (~c0_1(a149)) | c3_1(a128) | c1_1(a128) | c0_1(a128) | c2_1(a128) | c1_1(a128) | c0_1(a128))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a149) | c2_1(a149) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | c1_1(a128) | (~c0_1(a149)))),
% 0.79/0.97 inference(transitivity,[status(thm)],[2338, 2336])).
% 0.79/0.97 tff(2340,plain,
% 0.79/0.97 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a149) | c2_1(a149) | (~c0_1(a149)) | c3_1(a128) | c1_1(a128) | c0_1(a128) | c2_1(a128) | c1_1(a128) | c0_1(a128))),
% 0.79/0.97 inference(quant_inst,[status(thm)],[])).
% 0.79/0.97 tff(2341,plain,
% 0.79/0.97 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | c2_1(U) | (~c0_1(U)) | c3_1(V) | c1_1(V) | c0_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a149) | c2_1(a149) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | c1_1(a128) | (~c0_1(a149))),
% 0.79/0.97 inference(modus_ponens,[status(thm)],[2340, 2339])).
% 0.79/0.97 tff(2342,plain,
% 0.79/0.97 (c1_1(a128) | (~c0_1(a149))),
% 0.79/0.97 inference(unit_resolution,[status(thm)],[2341, 175, 596, 595, 2005, 2004, 2003, 460])).
% 0.79/0.97 tff(2343,plain,
% 0.79/0.97 (c1_1(a128)),
% 0.79/0.97 inference(unit_resolution,[status(thm)],[2342, 2335])).
% 0.79/0.97 tff(2344,plain,
% 0.79/0.97 (hskp16 | (~c3_1(a149)) | (~c0_1(a149))),
% 0.79/0.97 inference(unit_resolution,[status(thm)],[1293, 175, 53, 596, 138])).
% 0.79/0.97 tff(2345,plain,
% 0.79/0.97 (hskp16),
% 0.79/0.97 inference(unit_resolution,[status(thm)],[2344, 2335, 2283])).
% 0.79/0.97 tff(2346,plain,
% 0.79/0.97 (~c2_1(a151)),
% 0.79/0.97 inference(unit_resolution,[status(thm)],[188, 2345])).
% 0.79/0.97 tff(2347,plain,
% 0.79/0.97 (hskp17 | (~c3_1(a149)) | (~c0_1(a149))),
% 0.79/0.97 inference(unit_resolution,[status(thm)],[1886, 175, 1821, 1813, 1807, 595, 269])).
% 0.79/0.97 tff(2348,plain,
% 0.79/0.97 (hskp17),
% 0.79/0.97 inference(unit_resolution,[status(thm)],[2347, 2335, 2283])).
% 0.79/0.97 tff(2349,plain,
% 0.79/0.97 (~c3_1(a158)),
% 0.79/0.97 inference(unit_resolution,[status(thm)],[411, 2348])).
% 0.79/0.97 tff(2350,plain,
% 0.79/0.97 (~c2_1(a158)),
% 0.79/0.97 inference(unit_resolution,[status(thm)],[417, 2348])).
% 0.79/0.97 tff(2351,plain,
% 0.79/0.97 (c1_1(a158)),
% 0.79/0.97 inference(unit_resolution,[status(thm)],[425, 2348])).
% 0.79/0.97 tff(2352,plain,
% 0.79/0.97 (c1_1(a151)),
% 0.79/0.97 inference(unit_resolution,[status(thm)],[196, 2345])).
% 0.79/0.97 tff(2353,plain,
% 0.79/0.97 (c0_1(a151)),
% 0.79/0.97 inference(unit_resolution,[status(thm)],[231, 2345])).
% 0.79/0.97 tff(2354,assumption,(~hskp6), introduced(assumption)).
% 0.79/0.97 tff(2355,plain,
% 0.79/0.97 (hskp9),
% 0.79/0.97 inference(unit_resolution,[status(thm)],[753, 2354, 53])).
% 0.79/0.97 tff(2356,plain,
% 0.79/0.97 (~c3_1(a136)),
% 0.79/0.97 inference(unit_resolution,[status(thm)],[759, 2355])).
% 0.79/0.97 tff(2357,plain,
% 0.79/0.97 (c2_1(a136)),
% 0.79/0.97 inference(unit_resolution,[status(thm)],[767, 2355])).
% 0.79/0.97 tff(2358,plain,
% 0.79/0.97 (c0_1(a136)),
% 0.79/0.97 inference(unit_resolution,[status(thm)],[783, 2355])).
% 0.79/0.97 tff(2359,plain,
% 0.79/0.97 (~c1_1(a136)),
% 0.79/0.97 inference(unit_resolution,[status(thm)],[1337, 175, 11, 2358, 2357, 2356, 21])).
% 0.79/0.97 tff(2360,plain,
% 0.79/0.97 (~hskp5),
% 0.79/0.97 inference(unit_resolution,[status(thm)],[2325, 2359, 625, 2356, 2357])).
% 0.79/0.97 tff(2361,plain,
% 0.79/0.97 (((~![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp5 | hskp4 | c3_1(a136) | (~ndr1_0) | c1_1(a136) | (~c0_1(a136)))) <=> ((~![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | hskp5 | hskp4 | c3_1(a136) | (~ndr1_0) | c1_1(a136) | (~c0_1(a136)))),
% 0.79/0.97 inference(rewrite,[status(thm)],[])).
% 0.79/0.97 tff(2362,plain,
% 0.79/0.97 ((hskp5 | hskp4 | (~ndr1_0) | c3_1(a136) | c1_1(a136) | (~c0_1(a136))) <=> (hskp5 | hskp4 | c3_1(a136) | (~ndr1_0) | c1_1(a136) | (~c0_1(a136)))),
% 0.79/0.97 inference(rewrite,[status(thm)],[])).
% 0.79/0.97 tff(2363,plain,
% 0.79/0.97 (((~![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp5 | hskp4 | (~ndr1_0) | c3_1(a136) | c1_1(a136) | (~c0_1(a136)))) <=> ((~![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp5 | hskp4 | c3_1(a136) | (~ndr1_0) | c1_1(a136) | (~c0_1(a136))))),
% 0.79/0.97 inference(monotonicity,[status(thm)],[2362])).
% 0.79/0.97 tff(2364,plain,
% 0.79/0.97 (((~![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp5 | hskp4 | (~ndr1_0) | c3_1(a136) | c1_1(a136) | (~c0_1(a136)))) <=> ((~![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | hskp5 | hskp4 | c3_1(a136) | (~ndr1_0) | c1_1(a136) | (~c0_1(a136)))),
% 0.79/0.97 inference(transitivity,[status(thm)],[2363, 2361])).
% 0.79/0.97 tff(2365,plain,
% 0.79/0.97 ((~![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | (hskp5 | hskp4 | (~ndr1_0) | c3_1(a136) | c1_1(a136) | (~c0_1(a136)))),
% 0.79/0.97 inference(quant_inst,[status(thm)],[])).
% 0.79/0.97 tff(2366,plain,
% 0.79/0.97 ((~![U: $i] : (hskp5 | hskp4 | (~ndr1_0) | c3_1(U) | c1_1(U) | (~c0_1(U)))) | hskp5 | hskp4 | c3_1(a136) | (~ndr1_0) | c1_1(a136) | (~c0_1(a136))),
% 0.79/0.97 inference(modus_ponens,[status(thm)],[2365, 2364])).
% 0.79/0.97 tff(2367,plain,
% 0.79/0.97 (hskp5 | hskp4 | c1_1(a136)),
% 0.79/0.97 inference(unit_resolution,[status(thm)],[2366, 175, 2358, 2356, 2080])).
% 0.79/0.97 tff(2368,plain,
% 0.79/0.97 (hskp4),
% 0.79/0.97 inference(unit_resolution,[status(thm)],[2367, 2360, 2359])).
% 0.79/0.97 tff(2369,plain,
% 0.79/0.97 (~c3_1(a130)),
% 0.79/0.97 inference(unit_resolution,[status(thm)],[2173, 2368])).
% 0.79/0.97 tff(2370,plain,
% 0.79/0.97 (c2_1(a130)),
% 0.79/0.97 inference(unit_resolution,[status(thm)],[2181, 2368])).
% 0.79/0.97 tff(2371,plain,
% 0.79/0.97 (c1_1(a130)),
% 0.79/0.97 inference(unit_resolution,[status(thm)],[2197, 2368])).
% 0.79/0.97 tff(2372,plain,
% 0.79/0.97 (~c0_1(a130)),
% 0.79/0.97 inference(unit_resolution,[status(thm)],[2204, 175, 11, 2371, 2370, 2369, 21])).
% 0.79/0.97 tff(2373,assumption,(~c3_1(a158)), introduced(assumption)).
% 0.79/0.97 tff(2374,assumption,(~c2_1(a158)), introduced(assumption)).
% 0.79/0.97 tff(2375,assumption,(c1_1(a158)), introduced(assumption)).
% 0.79/0.97 tff(2376,plain,
% 0.79/0.97 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | (c2_1(a158) | c3_1(a158) | c2_1(a151) | c3_1(a136) | (~ndr1_0) | c1_1(a136) | (~c2_1(a136)) | (~c3_1(a151)) | (~c1_1(a151)) | (~c1_1(a158)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | c2_1(a158) | c3_1(a158) | c2_1(a151) | c3_1(a136) | (~ndr1_0) | c1_1(a136) | (~c2_1(a136)) | (~c3_1(a151)) | (~c1_1(a151)) | (~c1_1(a158)))),
% 0.79/0.97 inference(rewrite,[status(thm)],[])).
% 0.79/0.97 tff(2377,plain,
% 0.79/0.97 (((~ndr1_0) | c2_1(a151) | (~c3_1(a151)) | (~c1_1(a151)) | c3_1(a158) | c2_1(a158) | (~c1_1(a158)) | c1_1(a136) | c3_1(a136) | (~c2_1(a136))) <=> (c2_1(a158) | c3_1(a158) | c2_1(a151) | c3_1(a136) | (~ndr1_0) | c1_1(a136) | (~c2_1(a136)) | (~c3_1(a151)) | (~c1_1(a151)) | (~c1_1(a158)))),
% 0.79/0.97 inference(rewrite,[status(thm)],[])).
% 0.79/0.97 tff(2378,plain,
% 0.79/0.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a151) | (~c3_1(a151)) | (~c1_1(a151)) | c3_1(a158) | c2_1(a158) | (~c1_1(a158)) | c1_1(a136) | c3_1(a136) | (~c2_1(a136)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | (c2_1(a158) | c3_1(a158) | c2_1(a151) | c3_1(a136) | (~ndr1_0) | c1_1(a136) | (~c2_1(a136)) | (~c3_1(a151)) | (~c1_1(a151)) | (~c1_1(a158))))),
% 0.79/0.98 inference(monotonicity,[status(thm)],[2377])).
% 0.79/0.98 tff(2379,plain,
% 0.79/0.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a151) | (~c3_1(a151)) | (~c1_1(a151)) | c3_1(a158) | c2_1(a158) | (~c1_1(a158)) | c1_1(a136) | c3_1(a136) | (~c2_1(a136)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | c2_1(a158) | c3_1(a158) | c2_1(a151) | c3_1(a136) | (~ndr1_0) | c1_1(a136) | (~c2_1(a136)) | (~c3_1(a151)) | (~c1_1(a151)) | (~c1_1(a158)))),
% 0.79/0.98 inference(transitivity,[status(thm)],[2378, 2376])).
% 0.79/0.98 tff(2380,plain,
% 0.79/0.98 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a151) | (~c3_1(a151)) | (~c1_1(a151)) | c3_1(a158) | c2_1(a158) | (~c1_1(a158)) | c1_1(a136) | c3_1(a136) | (~c2_1(a136)))),
% 0.79/0.98 inference(quant_inst,[status(thm)],[])).
% 0.79/0.98 tff(2381,plain,
% 0.79/0.98 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | c2_1(a158) | c3_1(a158) | c2_1(a151) | c3_1(a136) | (~ndr1_0) | c1_1(a136) | (~c2_1(a136)) | (~c3_1(a151)) | (~c1_1(a151)) | (~c1_1(a158))),
% 0.79/0.98 inference(modus_ponens,[status(thm)],[2380, 2379])).
% 0.79/0.98 tff(2382,plain,
% 0.79/0.98 (~c3_1(a151)),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[2381, 175, 2375, 607, 2357, 2374, 2373, 597, 2356, 10, 2359])).
% 0.79/0.98 tff(2383,assumption,(c0_1(a151)), introduced(assumption)).
% 0.79/0.98 tff(2384,plain,
% 0.79/0.98 (((~![U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp12 | (~ndr1_0) | c3_1(a151) | (~c1_1(a151)) | (~c0_1(a151)))) <=> ((~![U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp12 | (~ndr1_0) | c3_1(a151) | (~c1_1(a151)) | (~c0_1(a151)))),
% 0.79/0.98 inference(rewrite,[status(thm)],[])).
% 0.79/0.98 tff(2385,plain,
% 0.79/0.98 ((~![U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | (hskp12 | (~ndr1_0) | c3_1(a151) | (~c1_1(a151)) | (~c0_1(a151)))),
% 0.79/0.98 inference(quant_inst,[status(thm)],[])).
% 0.79/0.98 tff(2386,plain,
% 0.79/0.98 ((~![U: $i] : (hskp12 | (~ndr1_0) | c3_1(U) | (~c1_1(U)) | (~c0_1(U)))) | hskp12 | (~ndr1_0) | c3_1(a151) | (~c1_1(a151)) | (~c0_1(a151))),
% 0.79/0.98 inference(modus_ponens,[status(thm)],[2385, 2384])).
% 0.79/0.98 tff(2387,plain,
% 0.79/0.98 (hskp12 | c3_1(a151)),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[2386, 175, 2383, 607, 224])).
% 0.79/0.98 tff(2388,plain,
% 0.79/0.98 (hskp12),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[2387, 2382])).
% 0.79/0.98 tff(2389,plain,
% 0.79/0.98 (~c0_1(a140)),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[593, 2388])).
% 0.79/0.98 tff(2390,plain,
% 0.79/0.98 (c3_1(a140)),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[604, 2388])).
% 0.79/0.98 tff(2391,plain,
% 0.79/0.98 (c1_1(a140)),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[801, 2388])).
% 0.79/0.98 tff(2392,plain,
% 0.79/0.98 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | c0_1(a140) | c3_1(a130) | (~ndr1_0) | (~c1_1(a130)) | c0_1(a130) | (~c3_1(a140)) | (~c1_1(a140)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp6 | c0_1(a140) | c3_1(a130) | (~ndr1_0) | (~c1_1(a130)) | c0_1(a130) | (~c3_1(a140)) | (~c1_1(a140)))),
% 0.79/0.98 inference(rewrite,[status(thm)],[])).
% 0.79/0.98 tff(2393,plain,
% 0.79/0.98 ((hskp6 | (~ndr1_0) | c0_1(a140) | (~c3_1(a140)) | (~c1_1(a140)) | c3_1(a130) | c0_1(a130) | (~c1_1(a130))) <=> (hskp6 | c0_1(a140) | c3_1(a130) | (~ndr1_0) | (~c1_1(a130)) | c0_1(a130) | (~c3_1(a140)) | (~c1_1(a140)))),
% 0.79/0.98 inference(rewrite,[status(thm)],[])).
% 0.79/0.98 tff(2394,plain,
% 0.79/0.98 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | (~ndr1_0) | c0_1(a140) | (~c3_1(a140)) | (~c1_1(a140)) | c3_1(a130) | c0_1(a130) | (~c1_1(a130)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | c0_1(a140) | c3_1(a130) | (~ndr1_0) | (~c1_1(a130)) | c0_1(a130) | (~c3_1(a140)) | (~c1_1(a140))))),
% 0.79/0.98 inference(monotonicity,[status(thm)],[2393])).
% 0.79/0.98 tff(2395,plain,
% 0.79/0.98 (((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | (~ndr1_0) | c0_1(a140) | (~c3_1(a140)) | (~c1_1(a140)) | c3_1(a130) | c0_1(a130) | (~c1_1(a130)))) <=> ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp6 | c0_1(a140) | c3_1(a130) | (~ndr1_0) | (~c1_1(a130)) | c0_1(a130) | (~c3_1(a140)) | (~c1_1(a140)))),
% 0.79/0.98 inference(transitivity,[status(thm)],[2394, 2392])).
% 0.79/0.98 tff(2396,plain,
% 0.79/0.98 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | (hskp6 | (~ndr1_0) | c0_1(a140) | (~c3_1(a140)) | (~c1_1(a140)) | c3_1(a130) | c0_1(a130) | (~c1_1(a130)))),
% 0.79/0.98 inference(quant_inst,[status(thm)],[])).
% 0.79/0.98 tff(2397,plain,
% 0.79/0.98 ((~![V: $i, U: $i] : (hskp6 | (~ndr1_0) | c0_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c1_1(V)))) | hskp6 | c0_1(a140) | c3_1(a130) | (~ndr1_0) | (~c1_1(a130)) | c0_1(a130) | (~c3_1(a140)) | (~c1_1(a140))),
% 0.79/0.98 inference(modus_ponens,[status(thm)],[2396, 2395])).
% 0.79/0.98 tff(2398,plain,
% 0.79/0.98 ($false),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[2397, 175, 2354, 2391, 2390, 2371, 2389, 2369, 315, 2372])).
% 0.79/0.98 tff(2399,plain,(hskp6 | (~c0_1(a151)) | (~c1_1(a151)) | hskp13 | (~c1_1(a158)) | c2_1(a158) | c3_1(a158) | c2_1(a151) | (~c1_1(a128)) | hskp21), inference(lemma,lemma(discharge,[]))).
% 0.79/0.98 tff(2400,plain,
% 0.79/0.98 (hskp6),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[2399, 2353, 2352, 11, 2351, 2350, 2349, 2346, 2343, 53])).
% 0.79/0.98 tff(2401,plain,
% 0.79/0.98 (~c2_1(a133)),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[336, 2400])).
% 0.79/0.98 tff(2402,plain,
% 0.79/0.98 (~c1_1(a133)),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[342, 2400])).
% 0.79/0.98 tff(2403,plain,
% 0.79/0.98 (~c0_1(a133)),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[348, 2400])).
% 0.79/0.98 tff(2404,plain,
% 0.79/0.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a149) | c0_1(a133) | c1_1(a133) | c2_1(a133) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c3_1(a149)) | (~c0_1(a149)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a149) | c0_1(a133) | c1_1(a133) | c2_1(a133) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c3_1(a149)) | (~c0_1(a149)))),
% 0.79/0.98 inference(rewrite,[status(thm)],[])).
% 0.79/0.98 tff(2405,plain,
% 0.79/0.98 (((~ndr1_0) | c1_1(a149) | (~c3_1(a149)) | (~c0_1(a149)) | c3_1(a128) | c0_1(a128) | c2_1(a128) | c2_1(a133) | c1_1(a133) | c0_1(a133)) <=> (c1_1(a149) | c0_1(a133) | c1_1(a133) | c2_1(a133) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c3_1(a149)) | (~c0_1(a149)))),
% 0.79/0.98 inference(rewrite,[status(thm)],[])).
% 0.79/0.98 tff(2406,plain,
% 0.79/0.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a149) | (~c3_1(a149)) | (~c0_1(a149)) | c3_1(a128) | c0_1(a128) | c2_1(a128) | c2_1(a133) | c1_1(a133) | c0_1(a133))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a149) | c0_1(a133) | c1_1(a133) | c2_1(a133) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c3_1(a149)) | (~c0_1(a149))))),
% 0.79/0.98 inference(monotonicity,[status(thm)],[2405])).
% 0.79/0.98 tff(2407,plain,
% 0.79/0.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a149) | (~c3_1(a149)) | (~c0_1(a149)) | c3_1(a128) | c0_1(a128) | c2_1(a128) | c2_1(a133) | c1_1(a133) | c0_1(a133))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a149) | c0_1(a133) | c1_1(a133) | c2_1(a133) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c3_1(a149)) | (~c0_1(a149)))),
% 0.79/0.98 inference(transitivity,[status(thm)],[2406, 2404])).
% 0.79/0.98 tff(2408,plain,
% 0.79/0.98 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a149) | (~c3_1(a149)) | (~c0_1(a149)) | c3_1(a128) | c0_1(a128) | c2_1(a128) | c2_1(a133) | c1_1(a133) | c0_1(a133))),
% 0.79/0.98 inference(quant_inst,[status(thm)],[])).
% 0.79/0.98 tff(2409,plain,
% 0.79/0.98 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a149) | c0_1(a133) | c1_1(a133) | c2_1(a133) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c3_1(a149)) | (~c0_1(a149))),
% 0.79/0.98 inference(modus_ponens,[status(thm)],[2408, 2407])).
% 0.79/0.98 tff(2410,plain,
% 0.79/0.98 ($false),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[2409, 175, 2283, 596, 2403, 2402, 2401, 2005, 2004, 2003, 258, 2335])).
% 0.79/0.98 tff(2411,plain,(hskp13 | c1_1(a149) | hskp21 | c2_1(a149)), inference(lemma,lemma(discharge,[]))).
% 0.79/0.98 tff(2412,plain,
% 0.79/0.98 (hskp13),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[2411, 596, 53, 595])).
% 0.79/0.98 tff(2413,plain,
% 0.79/0.98 (~c3_1(a144)),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[928, 2412])).
% 0.79/0.98 tff(2414,plain,
% 0.79/0.98 (~c0_1(a144)),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[949, 2412])).
% 0.79/0.98 tff(2415,plain,
% 0.79/0.98 (c2_1(a144)),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[936, 2412])).
% 0.79/0.98 tff(2416,plain,
% 0.79/0.98 (c1_1(a128)),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[1515, 2301, 1502, 1501, 2004, 2003, 1503])).
% 0.79/0.98 tff(2417,plain,
% 0.79/0.98 (~hskp11),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[2229, 2304, 2303, 2302, 1503, 1502, 1501])).
% 0.79/0.98 tff(2418,plain,
% 0.79/0.98 (hskp10),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[2231, 2417, 2416])).
% 0.79/0.98 tff(2419,plain,
% 0.79/0.98 (~c1_1(a138)),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[101, 2418])).
% 0.79/0.98 tff(2420,plain,
% 0.79/0.98 (c3_1(a138)),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[109, 2418])).
% 0.79/0.98 tff(2421,plain,
% 0.79/0.98 (c0_1(a138)),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[117, 2418])).
% 0.79/0.98 tff(2422,plain,
% 0.79/0.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a149) | c2_1(a149) | c1_1(a138) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c3_1(a138)) | (~c0_1(a138)) | c0_1(a149))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a149) | c2_1(a149) | c1_1(a138) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c3_1(a138)) | (~c0_1(a138)) | c0_1(a149))),
% 0.79/0.98 inference(rewrite,[status(thm)],[])).
% 0.79/0.98 tff(2423,plain,
% 0.79/0.98 (((~ndr1_0) | c1_1(a138) | (~c3_1(a138)) | (~c0_1(a138)) | c3_1(a128) | c0_1(a128) | c2_1(a128) | c2_1(a149) | c1_1(a149) | c0_1(a149)) <=> (c1_1(a149) | c2_1(a149) | c1_1(a138) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c3_1(a138)) | (~c0_1(a138)) | c0_1(a149))),
% 0.79/0.98 inference(rewrite,[status(thm)],[])).
% 0.79/0.98 tff(2424,plain,
% 0.79/0.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a138) | (~c3_1(a138)) | (~c0_1(a138)) | c3_1(a128) | c0_1(a128) | c2_1(a128) | c2_1(a149) | c1_1(a149) | c0_1(a149))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a149) | c2_1(a149) | c1_1(a138) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c3_1(a138)) | (~c0_1(a138)) | c0_1(a149)))),
% 0.79/0.98 inference(monotonicity,[status(thm)],[2423])).
% 0.79/0.98 tff(2425,plain,
% 0.79/0.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a138) | (~c3_1(a138)) | (~c0_1(a138)) | c3_1(a128) | c0_1(a128) | c2_1(a128) | c2_1(a149) | c1_1(a149) | c0_1(a149))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a149) | c2_1(a149) | c1_1(a138) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c3_1(a138)) | (~c0_1(a138)) | c0_1(a149))),
% 0.79/0.98 inference(transitivity,[status(thm)],[2424, 2422])).
% 0.79/0.98 tff(2426,plain,
% 0.79/0.98 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a138) | (~c3_1(a138)) | (~c0_1(a138)) | c3_1(a128) | c0_1(a128) | c2_1(a128) | c2_1(a149) | c1_1(a149) | c0_1(a149))),
% 0.79/0.98 inference(quant_inst,[status(thm)],[])).
% 0.79/0.98 tff(2427,plain,
% 0.79/0.98 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a149) | c2_1(a149) | c1_1(a138) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c3_1(a138)) | (~c0_1(a138)) | c0_1(a149)),
% 0.79/0.98 inference(modus_ponens,[status(thm)],[2426, 2425])).
% 0.79/0.98 tff(2428,plain,
% 0.79/0.98 ($false),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[2427, 175, 2421, 2420, 596, 595, 2419, 2005, 2004, 2003, 258, 1304])).
% 0.79/0.98 tff(2429,plain,(c0_1(a149) | c1_1(a149) | c2_1(a149) | (~c2_1(a144)) | c0_1(a144) | c3_1(a144)), inference(lemma,lemma(discharge,[]))).
% 0.79/0.98 tff(2430,plain,
% 0.79/0.98 (c0_1(a149)),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[2429, 596, 595, 2415, 2414, 2413])).
% 0.79/0.98 tff(2431,plain,
% 0.79/0.98 (hskp16),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[2344, 2430, 2283])).
% 0.79/0.98 tff(2432,plain,
% 0.79/0.98 (c0_1(a151)),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[231, 2431])).
% 0.79/0.98 tff(2433,plain,
% 0.79/0.98 (~c2_1(a151)),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[188, 2431])).
% 0.79/0.98 tff(2434,plain,
% 0.79/0.98 (hskp17),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[2347, 2430, 2283])).
% 0.79/0.98 tff(2435,plain,
% 0.79/0.98 (~c3_1(a158)),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[411, 2434])).
% 0.79/0.98 tff(2436,plain,
% 0.79/0.98 (~c2_1(a158)),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[417, 2434])).
% 0.79/0.98 tff(2437,plain,
% 0.79/0.98 (c1_1(a158)),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[425, 2434])).
% 0.79/0.98 tff(2438,plain,
% 0.79/0.98 (c1_1(a151)),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[196, 2431])).
% 0.79/0.98 tff(2439,plain,
% 0.79/0.98 (c1_1(a128)),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[2342, 2430])).
% 0.79/0.98 tff(2440,assumption,(~hskp12), introduced(assumption)).
% 0.79/0.98 tff(2441,plain,
% 0.79/0.98 (hskp12 | (~c1_1(a136))),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[790, 175, 1054, 1065, 224])).
% 0.79/0.98 tff(2442,plain,
% 0.79/0.98 (~c1_1(a136)),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[2441, 2440])).
% 0.79/0.98 tff(2443,plain,
% 0.79/0.98 (c3_1(a151)),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[2387, 2440])).
% 0.79/0.98 tff(2444,plain,
% 0.79/0.98 ($false),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[2381, 175, 2375, 607, 1053, 2374, 2373, 597, 1065, 10, 2443, 2442])).
% 0.79/0.98 tff(2445,plain,(hskp12 | (~c1_1(a158)) | (~c1_1(a151)) | (~c2_1(a136)) | c2_1(a158) | c3_1(a158) | c2_1(a151) | c3_1(a136) | (~c0_1(a136)) | (~c0_1(a151))), inference(lemma,lemma(discharge,[]))).
% 0.79/0.98 tff(2446,plain,
% 0.79/0.98 (hskp12),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[2445, 2357, 607, 2375, 2374, 2373, 597, 2356, 2358, 2383])).
% 0.79/0.98 tff(2447,plain,
% 0.79/0.98 (~c0_1(a140)),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[593, 2446])).
% 0.79/0.98 tff(2448,plain,
% 0.79/0.98 (c3_1(a140)),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[604, 2446])).
% 0.79/0.98 tff(2449,plain,
% 0.79/0.98 (c1_1(a140)),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[801, 2446])).
% 0.79/0.98 tff(2450,plain,
% 0.79/0.98 ($false),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[808, 175, 2354, 2449, 2448, 2447, 2005, 2003, 315, 625])).
% 0.79/0.98 tff(2451,plain,(hskp6 | (~c1_1(a128)) | (~c1_1(a151)) | (~c1_1(a158)) | c2_1(a158) | c3_1(a158) | c2_1(a151) | (~c0_1(a151)) | hskp21), inference(lemma,lemma(discharge,[]))).
% 0.79/0.98 tff(2452,plain,
% 0.79/0.98 (hskp6),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[2451, 2439, 2438, 2437, 2436, 2435, 2433, 2432, 53])).
% 0.79/0.98 tff(2453,plain,
% 0.79/0.98 (~c2_1(a133)),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[336, 2452])).
% 0.79/0.98 tff(2454,plain,
% 0.79/0.98 (~c1_1(a133)),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[342, 2452])).
% 0.79/0.98 tff(2455,plain,
% 0.79/0.98 (~c0_1(a133)),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[348, 2452])).
% 0.79/0.98 tff(2456,plain,
% 0.79/0.98 ($false),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[2409, 175, 2283, 596, 2455, 2454, 2453, 2005, 2004, 2003, 258, 2430])).
% 0.79/0.98 tff(2457,plain,(c1_1(a149) | hskp21 | c2_1(a149)), inference(lemma,lemma(discharge,[]))).
% 0.79/0.98 tff(2458,plain,
% 0.79/0.98 (hskp21),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[2457, 2239, 2238])).
% 0.79/0.98 tff(2459,plain,
% 0.79/0.98 (~c2_1(a170)),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[291, 2458])).
% 0.79/0.98 tff(2460,plain,
% 0.79/0.98 (~c0_1(a170)),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[297, 2458])).
% 0.79/0.98 tff(2461,plain,
% 0.79/0.98 (c3_1(a170)),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[322, 2458])).
% 0.79/0.98 tff(2462,plain,
% 0.79/0.98 (hskp9),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[1660, 175, 2461, 2460, 2459, 2005, 2004, 2003, 31])).
% 0.79/0.98 tff(2463,plain,
% 0.79/0.98 (~c3_1(a136)),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[759, 2462])).
% 0.79/0.98 tff(2464,plain,
% 0.79/0.98 (c2_1(a136)),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[767, 2462])).
% 0.79/0.98 tff(2465,plain,
% 0.79/0.98 (c0_1(a136)),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[783, 2462])).
% 0.79/0.98 tff(2466,plain,
% 0.79/0.98 (hskp13 | (~c1_1(a136))),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[1337, 175, 2465, 2464, 2463, 21])).
% 0.79/0.98 tff(2467,plain,
% 0.79/0.98 (~c1_1(a136)),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[2466, 11])).
% 0.79/0.98 tff(2468,plain,
% 0.79/0.98 (c0_1(a149) | hskp13),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[2334, 2239, 2238])).
% 0.79/0.98 tff(2469,plain,
% 0.79/0.98 (c0_1(a149)),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[2468, 11])).
% 0.79/0.98 tff(2470,plain,
% 0.79/0.98 (c3_1(a149)),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[246, 2237])).
% 0.79/0.98 tff(2471,plain,
% 0.79/0.98 (c1_1(a128) | (~c0_1(a149))),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[1578, 175, 2470, 2238, 2005, 2004, 2003, 258])).
% 0.79/0.98 tff(2472,plain,
% 0.79/0.98 (c1_1(a128)),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[2471, 2469])).
% 0.79/0.98 tff(2473,plain,
% 0.79/0.98 ((~hskp5) | (~c1_1(a128)) | c1_1(a136)),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[2325, 2463, 2464])).
% 0.79/0.98 tff(2474,plain,
% 0.79/0.98 (~hskp5),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[2473, 2472, 2467])).
% 0.79/0.98 tff(2475,plain,
% 0.79/0.98 (hskp5 | hskp4 | c1_1(a136)),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[2366, 175, 2465, 2463, 2080])).
% 0.79/0.98 tff(2476,plain,
% 0.79/0.98 (hskp4),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[2475, 2474, 2467])).
% 0.79/0.98 tff(2477,plain,
% 0.79/0.98 (hskp27),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[1782, 175, 2461, 2460, 2459, 2005, 2004, 2003, 1131])).
% 0.79/0.98 tff(2478,plain,
% 0.79/0.98 (c1_1(a137)),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[1162, 2477])).
% 0.79/0.98 tff(2479,plain,
% 0.79/0.98 (c3_1(a137)),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[1146, 2477])).
% 0.79/0.98 tff(2480,plain,
% 0.79/0.98 (c2_1(a137)),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[1154, 2477])).
% 0.79/0.98 tff(2481,plain,
% 0.79/0.98 ((~hskp4) | hskp13 | c1_1(a159)),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[2206, 2480, 2479, 2478])).
% 0.79/0.98 tff(2482,plain,
% 0.79/0.98 (c1_1(a159)),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[2481, 2476, 11])).
% 0.79/0.98 tff(2483,plain,
% 0.79/0.98 ($false),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[2310, 175, 2478, 2480, 2479, 1821, 2464, 1813, 2463, 94, 2467, 2482])).
% 0.79/0.98 tff(2484,plain,(hskp13), inference(lemma,lemma(discharge,[]))).
% 0.79/0.98 tff(2485,plain,
% 0.79/0.98 (~c3_1(a144)),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[928, 2484])).
% 0.79/0.98 tff(2486,plain,
% 0.79/0.98 (~c0_1(a144)),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[949, 2484])).
% 0.79/0.98 tff(2487,plain,
% 0.79/0.98 (c2_1(a144)),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[936, 2484])).
% 0.79/0.98 tff(2488,plain,
% 0.79/0.98 (c0_1(a149) | (~c2_1(a144)) | c0_1(a144) | c3_1(a144)),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[2429, 2239, 2238])).
% 0.79/0.98 tff(2489,plain,
% 0.79/0.98 (c0_1(a149)),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[2488, 2487, 2486, 2485])).
% 0.79/0.98 tff(2490,assumption,(hskp24), introduced(assumption)).
% 0.79/0.98 tff(2491,plain,
% 0.79/0.98 (((~hskp24) | (~c3_1(a183))) <=> ((~hskp24) | (~c3_1(a183)))),
% 0.79/0.98 inference(rewrite,[status(thm)],[])).
% 0.79/0.98 tff(2492,plain,
% 0.79/0.98 (((~c3_1(a183)) | (~hskp24)) <=> ((~hskp24) | (~c3_1(a183)))),
% 0.79/0.98 inference(rewrite,[status(thm)],[])).
% 0.79/0.98 tff(2493,axiom,((~c3_1(a183)) | (~hskp24)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause90')).
% 0.79/0.98 tff(2494,plain,
% 0.79/0.98 ((~hskp24) | (~c3_1(a183))),
% 0.79/0.98 inference(modus_ponens,[status(thm)],[2493, 2492])).
% 0.79/0.98 tff(2495,plain,
% 0.79/0.98 ((~hskp24) | (~c3_1(a183))),
% 0.79/0.98 inference(modus_ponens,[status(thm)],[2494, 2491])).
% 0.79/0.98 tff(2496,plain,
% 0.79/0.98 (~c3_1(a183)),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[2495, 2490])).
% 0.79/0.98 tff(2497,plain,
% 0.79/0.98 (~c2_1(a183)),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[2144, 2490])).
% 0.79/0.98 tff(2498,plain,
% 0.79/0.98 (~c1_1(a183)),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[2150, 2490])).
% 0.79/0.98 tff(2499,plain,
% 0.79/0.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c1_1(a183) | c2_1(a183) | c3_1(a183) | c0_1(a144) | c3_1(a144) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | (~c2_1(a144)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c1_1(a183) | c2_1(a183) | c3_1(a183) | c0_1(a144) | c3_1(a144) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | (~c2_1(a144)))),
% 0.79/0.98 inference(rewrite,[status(thm)],[])).
% 0.79/0.98 tff(2500,plain,
% 0.79/0.98 (((~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | c3_1(a144) | c0_1(a144) | (~c2_1(a144)) | c2_1(a183) | c1_1(a183) | c3_1(a183)) <=> (c1_1(a183) | c2_1(a183) | c3_1(a183) | c0_1(a144) | c3_1(a144) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | (~c2_1(a144)))),
% 0.79/0.98 inference(rewrite,[status(thm)],[])).
% 0.79/0.98 tff(2501,plain,
% 0.79/0.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | c3_1(a144) | c0_1(a144) | (~c2_1(a144)) | c2_1(a183) | c1_1(a183) | c3_1(a183))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | (c1_1(a183) | c2_1(a183) | c3_1(a183) | c0_1(a144) | c3_1(a144) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | (~c2_1(a144))))),
% 0.79/0.98 inference(monotonicity,[status(thm)],[2500])).
% 0.79/0.98 tff(2502,plain,
% 0.79/0.98 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | c3_1(a144) | c0_1(a144) | (~c2_1(a144)) | c2_1(a183) | c1_1(a183) | c3_1(a183))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c1_1(a183) | c2_1(a183) | c3_1(a183) | c0_1(a144) | c3_1(a144) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | (~c2_1(a144)))),
% 0.79/0.98 inference(transitivity,[status(thm)],[2501, 2499])).
% 0.79/0.98 tff(2503,plain,
% 0.79/0.98 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | ((~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | c3_1(a144) | c0_1(a144) | (~c2_1(a144)) | c2_1(a183) | c1_1(a183) | c3_1(a183))),
% 0.79/0.98 inference(quant_inst,[status(thm)],[])).
% 0.79/0.98 tff(2504,plain,
% 0.79/0.98 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | (~c2_1(U)) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c0_1(V) | (~c2_1(V)) | c2_1(W) | c1_1(W) | c3_1(W))) | c1_1(a183) | c2_1(a183) | c3_1(a183) | c0_1(a144) | c3_1(a144) | (~ndr1_0) | (~c2_1(a137)) | (~c3_1(a137)) | (~c1_1(a137)) | (~c2_1(a144))),
% 0.79/0.98 inference(modus_ponens,[status(thm)],[2503, 2502])).
% 0.79/0.98 tff(2505,plain,
% 0.79/0.98 ($false),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[2504, 175, 2183, 2114, 2113, 1503, 2498, 2497, 2496, 1502, 1501, 1104])).
% 0.79/0.98 tff(2506,plain,((~hskp24) | (~c1_1(a137)) | (~c2_1(a137)) | (~c3_1(a137)) | (~c2_1(a144)) | c0_1(a144) | c3_1(a144)), inference(lemma,lemma(discharge,[]))).
% 0.79/0.98 tff(2507,plain,
% 0.79/0.98 ((~hskp24) | (~c2_1(a144)) | c0_1(a144) | c3_1(a144)),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[2506, 2480, 2479, 2478])).
% 0.79/0.98 tff(2508,plain,
% 0.79/0.98 (~hskp24),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[2507, 2486, 2487, 2485])).
% 0.79/0.98 tff(2509,plain,
% 0.79/0.98 (^[U: $i] : refl((hskp24 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> (hskp24 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))))),
% 0.79/0.98 inference(bind,[status(th)],[])).
% 0.79/0.98 tff(2510,plain,
% 0.79/0.98 (![U: $i] : (hskp24 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp24 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.79/0.98 inference(quant_intro,[status(thm)],[2509])).
% 0.79/0.98 tff(2511,plain,
% 0.79/0.98 (![U: $i] : (hskp24 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) <=> ![U: $i] : (hskp24 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.79/0.98 inference(rewrite,[status(thm)],[])).
% 0.79/0.98 tff(2512,plain,
% 0.79/0.98 (^[U: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) <=> ((~ndr1_0) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> (((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c2_1(U)))), rewrite((((~ndr1_0) | (~c3_1(U)) | (~c0_1(U))) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) <=> ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp5) <=> (((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp5))), rewrite((((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp5) <=> (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))), ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp5) <=> (hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp5) | hskp24) <=> ((hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp24))), rewrite(((hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U))) | hskp24) <=> (hskp24 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))), (((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp5) | hskp24) <=> (hskp24 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))))),
% 0.79/0.98 inference(bind,[status(th)],[])).
% 0.79/0.98 tff(2513,plain,
% 0.79/0.98 (![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp5) | hskp24) <=> ![U: $i] : (hskp24 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.79/0.98 inference(quant_intro,[status(thm)],[2512])).
% 0.79/0.98 tff(2514,axiom,(![U: $i] : ((((((~c0_1(U)) | (~c3_1(U))) | (~ndr1_0)) | c2_1(U)) | hskp5) | hskp24)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','clause152')).
% 0.79/0.98 tff(2515,plain,
% 0.79/0.98 (![U: $i] : (hskp24 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.79/0.98 inference(modus_ponens,[status(thm)],[2514, 2513])).
% 0.79/0.98 tff(2516,plain,
% 0.79/0.98 (![U: $i] : (hskp24 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.79/0.98 inference(modus_ponens,[status(thm)],[2515, 2511])).
% 0.79/0.98 tff(2517,plain,(
% 0.79/0.98 ![U: $i] : (hskp24 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.79/0.98 inference(skolemize,[status(sab)],[2516])).
% 0.79/0.98 tff(2518,plain,
% 0.79/0.98 (![U: $i] : (hskp24 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))),
% 0.79/0.98 inference(modus_ponens,[status(thm)],[2517, 2510])).
% 0.79/0.98 tff(2519,plain,
% 0.79/0.98 (((~![U: $i] : (hskp24 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp24 | hskp5 | c2_1(a149) | (~ndr1_0) | (~c3_1(a149)) | (~c0_1(a149)))) <=> ((~![U: $i] : (hskp24 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp24 | hskp5 | c2_1(a149) | (~ndr1_0) | (~c3_1(a149)) | (~c0_1(a149)))),
% 0.79/0.98 inference(rewrite,[status(thm)],[])).
% 0.79/0.98 tff(2520,plain,
% 0.79/0.98 ((hskp24 | hskp5 | (~ndr1_0) | c2_1(a149) | (~c3_1(a149)) | (~c0_1(a149))) <=> (hskp24 | hskp5 | c2_1(a149) | (~ndr1_0) | (~c3_1(a149)) | (~c0_1(a149)))),
% 0.79/0.98 inference(rewrite,[status(thm)],[])).
% 0.79/0.98 tff(2521,plain,
% 0.79/0.98 (((~![U: $i] : (hskp24 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp24 | hskp5 | (~ndr1_0) | c2_1(a149) | (~c3_1(a149)) | (~c0_1(a149)))) <=> ((~![U: $i] : (hskp24 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp24 | hskp5 | c2_1(a149) | (~ndr1_0) | (~c3_1(a149)) | (~c0_1(a149))))),
% 0.79/0.98 inference(monotonicity,[status(thm)],[2520])).
% 0.79/0.98 tff(2522,plain,
% 0.79/0.98 (((~![U: $i] : (hskp24 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp24 | hskp5 | (~ndr1_0) | c2_1(a149) | (~c3_1(a149)) | (~c0_1(a149)))) <=> ((~![U: $i] : (hskp24 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp24 | hskp5 | c2_1(a149) | (~ndr1_0) | (~c3_1(a149)) | (~c0_1(a149)))),
% 0.79/0.98 inference(transitivity,[status(thm)],[2521, 2519])).
% 0.79/0.98 tff(2523,plain,
% 0.79/0.98 ((~![U: $i] : (hskp24 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | (hskp24 | hskp5 | (~ndr1_0) | c2_1(a149) | (~c3_1(a149)) | (~c0_1(a149)))),
% 0.79/0.98 inference(quant_inst,[status(thm)],[])).
% 0.79/0.98 tff(2524,plain,
% 0.79/0.98 ((~![U: $i] : (hskp24 | hskp5 | (~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c0_1(U)))) | hskp24 | hskp5 | c2_1(a149) | (~ndr1_0) | (~c3_1(a149)) | (~c0_1(a149))),
% 0.79/0.98 inference(modus_ponens,[status(thm)],[2523, 2522])).
% 0.79/0.98 tff(2525,plain,
% 0.79/0.98 (hskp24 | hskp5 | (~c0_1(a149))),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[2524, 175, 2470, 2239, 2518])).
% 0.79/0.98 tff(2526,plain,
% 0.79/0.98 (hskp5),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[2525, 2508, 2489])).
% 0.79/0.98 tff(2527,plain,
% 0.79/0.98 (~c2_1(a131)),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[2093, 2526])).
% 0.79/0.98 tff(2528,plain,
% 0.79/0.98 (hskp17 | (~c0_1(a149))),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[1886, 175, 1821, 2470, 1813, 1807, 2239, 269])).
% 0.79/0.98 tff(2529,plain,
% 0.79/0.98 (hskp17),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[2528, 2489])).
% 0.79/0.98 tff(2530,plain,
% 0.79/0.98 (~c3_1(a158)),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[411, 2529])).
% 0.79/0.98 tff(2531,plain,
% 0.79/0.98 (~c2_1(a158)),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[417, 2529])).
% 0.79/0.98 tff(2532,plain,
% 0.79/0.98 ((~c2_1(a144)) | c0_1(a144) | c3_1(a144) | c1_1(a128)),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[1515, 2477, 2004, 2003])).
% 0.79/0.98 tff(2533,plain,
% 0.79/0.98 (c1_1(a128)),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[2532, 2486, 2485, 2487])).
% 0.79/0.98 tff(2534,plain,
% 0.79/0.98 (c1_1(a136)),
% 0.79/0.98 inference(unit_resolution,[status(thm)],[2473, 2526, 2533])).
% 0.79/0.98 tff(2535,plain,
% 0.79/0.98 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp22 | c2_1(a149) | (~ndr1_0) | (~c1_1(a136)) | (~c0_1(a136)) | (~c2_1(a136)) | (~c3_1(a149)) | (~c0_1(a149)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp22 | c2_1(a149) | (~ndr1_0) | (~c1_1(a136)) | (~c0_1(a136)) | (~c2_1(a136)) | (~c3_1(a149)) | (~c0_1(a149)))),
% 0.79/0.98 inference(rewrite,[status(thm)],[])).
% 0.79/0.98 tff(2536,plain,
% 0.79/0.98 ((hskp22 | (~ndr1_0) | (~c2_1(a136)) | (~c1_1(a136)) | (~c0_1(a136)) | c2_1(a149) | (~c3_1(a149)) | (~c0_1(a149))) <=> (hskp22 | c2_1(a149) | (~ndr1_0) | (~c1_1(a136)) | (~c0_1(a136)) | (~c2_1(a136)) | (~c3_1(a149)) | (~c0_1(a149)))),
% 0.79/0.98 inference(rewrite,[status(thm)],[])).
% 0.79/0.98 tff(2537,plain,
% 0.79/0.98 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | (~c2_1(a136)) | (~c1_1(a136)) | (~c0_1(a136)) | c2_1(a149) | (~c3_1(a149)) | (~c0_1(a149)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp22 | c2_1(a149) | (~ndr1_0) | (~c1_1(a136)) | (~c0_1(a136)) | (~c2_1(a136)) | (~c3_1(a149)) | (~c0_1(a149))))),
% 0.79/0.99 inference(monotonicity,[status(thm)],[2536])).
% 0.79/0.99 tff(2538,plain,
% 0.79/0.99 (((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | (~c2_1(a136)) | (~c1_1(a136)) | (~c0_1(a136)) | c2_1(a149) | (~c3_1(a149)) | (~c0_1(a149)))) <=> ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp22 | c2_1(a149) | (~ndr1_0) | (~c1_1(a136)) | (~c0_1(a136)) | (~c2_1(a136)) | (~c3_1(a149)) | (~c0_1(a149)))),
% 0.79/0.99 inference(transitivity,[status(thm)],[2537, 2535])).
% 0.79/0.99 tff(2539,plain,
% 0.79/0.99 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | (hskp22 | (~ndr1_0) | (~c2_1(a136)) | (~c1_1(a136)) | (~c0_1(a136)) | c2_1(a149) | (~c3_1(a149)) | (~c0_1(a149)))),
% 0.79/0.99 inference(quant_inst,[status(thm)],[])).
% 0.79/0.99 tff(2540,plain,
% 0.79/0.99 ((~![V: $i, U: $i] : (hskp22 | (~ndr1_0) | (~c2_1(U)) | (~c1_1(U)) | (~c0_1(U)) | c2_1(V) | (~c3_1(V)) | (~c0_1(V)))) | hskp22 | c2_1(a149) | (~ndr1_0) | (~c1_1(a136)) | (~c0_1(a136)) | (~c2_1(a136)) | (~c3_1(a149)) | (~c0_1(a149))),
% 0.79/0.99 inference(modus_ponens,[status(thm)],[2539, 2538])).
% 0.79/0.99 tff(2541,plain,
% 0.79/0.99 (hskp22 | (~c1_1(a136)) | (~c0_1(a149))),
% 0.79/0.99 inference(unit_resolution,[status(thm)],[2540, 175, 2470, 2465, 2464, 2239, 976])).
% 0.79/0.99 tff(2542,plain,
% 0.79/0.99 (hskp22),
% 0.79/0.99 inference(unit_resolution,[status(thm)],[2541, 2534, 2489])).
% 0.79/0.99 tff(2543,plain,
% 0.79/0.99 (~c1_1(a179)),
% 0.79/0.99 inference(unit_resolution,[status(thm)],[989, 2542])).
% 0.79/0.99 tff(2544,plain,
% 0.79/0.99 (c3_1(a131)),
% 0.79/0.99 inference(unit_resolution,[status(thm)],[2103, 2526])).
% 0.79/0.99 tff(2545,plain,
% 0.79/0.99 (c1_1(a131)),
% 0.79/0.99 inference(unit_resolution,[status(thm)],[2111, 2526])).
% 0.79/0.99 tff(2546,plain,
% 0.79/0.99 (c1_1(a158)),
% 0.79/0.99 inference(unit_resolution,[status(thm)],[425, 2529])).
% 0.79/0.99 tff(2547,plain,
% 0.79/0.99 (c2_1(a179)),
% 0.79/0.99 inference(unit_resolution,[status(thm)],[997, 2542])).
% 0.79/0.99 tff(2548,plain,
% 0.79/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | (c1_1(a179) | c2_1(a158) | c3_1(a158) | c2_1(a131) | (~ndr1_0) | (~c3_1(a131)) | (~c1_1(a131)) | (~c1_1(a158)) | c3_1(a179) | (~c2_1(a179)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | c1_1(a179) | c2_1(a158) | c3_1(a158) | c2_1(a131) | (~ndr1_0) | (~c3_1(a131)) | (~c1_1(a131)) | (~c1_1(a158)) | c3_1(a179) | (~c2_1(a179)))),
% 0.79/0.99 inference(rewrite,[status(thm)],[])).
% 0.79/0.99 tff(2549,plain,
% 0.79/0.99 (((~ndr1_0) | c2_1(a131) | (~c3_1(a131)) | (~c1_1(a131)) | c3_1(a158) | c2_1(a158) | (~c1_1(a158)) | c1_1(a179) | c3_1(a179) | (~c2_1(a179))) <=> (c1_1(a179) | c2_1(a158) | c3_1(a158) | c2_1(a131) | (~ndr1_0) | (~c3_1(a131)) | (~c1_1(a131)) | (~c1_1(a158)) | c3_1(a179) | (~c2_1(a179)))),
% 0.79/0.99 inference(rewrite,[status(thm)],[])).
% 0.79/0.99 tff(2550,plain,
% 0.79/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a131) | (~c3_1(a131)) | (~c1_1(a131)) | c3_1(a158) | c2_1(a158) | (~c1_1(a158)) | c1_1(a179) | c3_1(a179) | (~c2_1(a179)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | (c1_1(a179) | c2_1(a158) | c3_1(a158) | c2_1(a131) | (~ndr1_0) | (~c3_1(a131)) | (~c1_1(a131)) | (~c1_1(a158)) | c3_1(a179) | (~c2_1(a179))))),
% 0.79/0.99 inference(monotonicity,[status(thm)],[2549])).
% 0.79/0.99 tff(2551,plain,
% 0.79/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a131) | (~c3_1(a131)) | (~c1_1(a131)) | c3_1(a158) | c2_1(a158) | (~c1_1(a158)) | c1_1(a179) | c3_1(a179) | (~c2_1(a179)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | c1_1(a179) | c2_1(a158) | c3_1(a158) | c2_1(a131) | (~ndr1_0) | (~c3_1(a131)) | (~c1_1(a131)) | (~c1_1(a158)) | c3_1(a179) | (~c2_1(a179)))),
% 0.79/0.99 inference(transitivity,[status(thm)],[2550, 2548])).
% 0.79/0.99 tff(2552,plain,
% 0.79/0.99 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | ((~ndr1_0) | c2_1(a131) | (~c3_1(a131)) | (~c1_1(a131)) | c3_1(a158) | c2_1(a158) | (~c1_1(a158)) | c1_1(a179) | c3_1(a179) | (~c2_1(a179)))),
% 0.79/0.99 inference(quant_inst,[status(thm)],[])).
% 0.79/0.99 tff(2553,plain,
% 0.79/0.99 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c2_1(U) | (~c3_1(U)) | (~c1_1(U)) | c3_1(V) | c2_1(V) | (~c1_1(V)) | c1_1(W) | c3_1(W) | (~c2_1(W)))) | c1_1(a179) | c2_1(a158) | c3_1(a158) | c2_1(a131) | (~ndr1_0) | (~c3_1(a131)) | (~c1_1(a131)) | (~c1_1(a158)) | c3_1(a179) | (~c2_1(a179))),
% 0.79/0.99 inference(modus_ponens,[status(thm)],[2552, 2551])).
% 0.79/0.99 tff(2554,plain,
% 0.79/0.99 (c3_1(a179)),
% 0.79/0.99 inference(unit_resolution,[status(thm)],[2553, 175, 2547, 2546, 2545, 2544, 2543, 2531, 2530, 2527, 10])).
% 0.79/0.99 tff(2555,plain,
% 0.79/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a170) | c2_1(a170) | c1_1(a149) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c3_1(a149)) | (~c0_1(a149)) | c1_1(a170))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a170) | c2_1(a170) | c1_1(a149) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c3_1(a149)) | (~c0_1(a149)) | c1_1(a170))),
% 0.79/0.99 inference(rewrite,[status(thm)],[])).
% 0.79/0.99 tff(2556,plain,
% 0.79/0.99 (((~ndr1_0) | c1_1(a149) | (~c3_1(a149)) | (~c0_1(a149)) | c3_1(a128) | c0_1(a128) | c2_1(a128) | c2_1(a170) | c1_1(a170) | c0_1(a170)) <=> (c0_1(a170) | c2_1(a170) | c1_1(a149) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c3_1(a149)) | (~c0_1(a149)) | c1_1(a170))),
% 0.79/0.99 inference(rewrite,[status(thm)],[])).
% 0.79/0.99 tff(2557,plain,
% 0.79/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a149) | (~c3_1(a149)) | (~c0_1(a149)) | c3_1(a128) | c0_1(a128) | c2_1(a128) | c2_1(a170) | c1_1(a170) | c0_1(a170))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c0_1(a170) | c2_1(a170) | c1_1(a149) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c3_1(a149)) | (~c0_1(a149)) | c1_1(a170)))),
% 0.79/0.99 inference(monotonicity,[status(thm)],[2556])).
% 0.79/0.99 tff(2558,plain,
% 0.79/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a149) | (~c3_1(a149)) | (~c0_1(a149)) | c3_1(a128) | c0_1(a128) | c2_1(a128) | c2_1(a170) | c1_1(a170) | c0_1(a170))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a170) | c2_1(a170) | c1_1(a149) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c3_1(a149)) | (~c0_1(a149)) | c1_1(a170))),
% 0.79/0.99 inference(transitivity,[status(thm)],[2557, 2555])).
% 0.79/0.99 tff(2559,plain,
% 0.79/0.99 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a149) | (~c3_1(a149)) | (~c0_1(a149)) | c3_1(a128) | c0_1(a128) | c2_1(a128) | c2_1(a170) | c1_1(a170) | c0_1(a170))),
% 0.79/0.99 inference(quant_inst,[status(thm)],[])).
% 0.79/0.99 tff(2560,plain,
% 0.79/0.99 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c0_1(a170) | c2_1(a170) | c1_1(a149) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c3_1(a149)) | (~c0_1(a149)) | c1_1(a170)),
% 0.79/0.99 inference(modus_ponens,[status(thm)],[2559, 2558])).
% 0.79/0.99 tff(2561,plain,
% 0.79/0.99 ((~c0_1(a149)) | c1_1(a170)),
% 0.79/0.99 inference(unit_resolution,[status(thm)],[2560, 175, 2470, 2460, 2459, 2238, 2005, 2004, 2003, 258])).
% 0.79/0.99 tff(2562,plain,
% 0.79/0.99 (c1_1(a170)),
% 0.79/0.99 inference(unit_resolution,[status(thm)],[2561, 2489])).
% 0.79/0.99 tff(2563,plain,
% 0.79/0.99 (hskp6 | (~c1_1(a128)) | (~c1_1(a170))),
% 0.79/0.99 inference(unit_resolution,[status(thm)],[329, 175, 2461, 2460, 2005, 2003, 315])).
% 0.79/0.99 tff(2564,plain,
% 0.79/0.99 (hskp6),
% 0.79/0.99 inference(unit_resolution,[status(thm)],[2563, 2533, 2562])).
% 0.79/0.99 tff(2565,plain,
% 0.79/0.99 (~c2_1(a133)),
% 0.79/0.99 inference(unit_resolution,[status(thm)],[336, 2564])).
% 0.79/0.99 tff(2566,plain,
% 0.79/0.99 (~c1_1(a133)),
% 0.79/0.99 inference(unit_resolution,[status(thm)],[342, 2564])).
% 0.79/0.99 tff(2567,plain,
% 0.79/0.99 (~c0_1(a133)),
% 0.79/0.99 inference(unit_resolution,[status(thm)],[348, 2564])).
% 0.79/0.99 tff(2568,plain,
% 0.79/0.99 (c0_1(a179)),
% 0.79/0.99 inference(unit_resolution,[status(thm)],[1005, 2542])).
% 0.79/0.99 tff(2569,plain,
% 0.79/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a179) | c0_1(a133) | c1_1(a133) | c2_1(a133) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c3_1(a179)) | (~c0_1(a179)))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a179) | c0_1(a133) | c1_1(a133) | c2_1(a133) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c3_1(a179)) | (~c0_1(a179)))),
% 0.79/0.99 inference(rewrite,[status(thm)],[])).
% 0.79/0.99 tff(2570,plain,
% 0.79/0.99 (((~ndr1_0) | c1_1(a179) | (~c3_1(a179)) | (~c0_1(a179)) | c3_1(a128) | c0_1(a128) | c2_1(a128) | c2_1(a133) | c1_1(a133) | c0_1(a133)) <=> (c1_1(a179) | c0_1(a133) | c1_1(a133) | c2_1(a133) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c3_1(a179)) | (~c0_1(a179)))),
% 0.79/0.99 inference(rewrite,[status(thm)],[])).
% 0.79/0.99 tff(2571,plain,
% 0.79/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a179) | (~c3_1(a179)) | (~c0_1(a179)) | c3_1(a128) | c0_1(a128) | c2_1(a128) | c2_1(a133) | c1_1(a133) | c0_1(a133))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | (c1_1(a179) | c0_1(a133) | c1_1(a133) | c2_1(a133) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c3_1(a179)) | (~c0_1(a179))))),
% 0.79/0.99 inference(monotonicity,[status(thm)],[2570])).
% 0.79/0.99 tff(2572,plain,
% 0.79/0.99 (((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a179) | (~c3_1(a179)) | (~c0_1(a179)) | c3_1(a128) | c0_1(a128) | c2_1(a128) | c2_1(a133) | c1_1(a133) | c0_1(a133))) <=> ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a179) | c0_1(a133) | c1_1(a133) | c2_1(a133) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c3_1(a179)) | (~c0_1(a179)))),
% 0.79/0.99 inference(transitivity,[status(thm)],[2571, 2569])).
% 0.79/0.99 tff(2573,plain,
% 0.79/0.99 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | ((~ndr1_0) | c1_1(a179) | (~c3_1(a179)) | (~c0_1(a179)) | c3_1(a128) | c0_1(a128) | c2_1(a128) | c2_1(a133) | c1_1(a133) | c0_1(a133))),
% 0.79/0.99 inference(quant_inst,[status(thm)],[])).
% 0.79/0.99 tff(2574,plain,
% 0.79/0.99 ((~![W: $i, V: $i, U: $i] : ((~ndr1_0) | c1_1(U) | (~c3_1(U)) | (~c0_1(U)) | c3_1(V) | c0_1(V) | c2_1(V) | c2_1(W) | c1_1(W) | c0_1(W))) | c1_1(a179) | c0_1(a133) | c1_1(a133) | c2_1(a133) | c0_1(a128) | c2_1(a128) | c3_1(a128) | (~ndr1_0) | (~c3_1(a179)) | (~c0_1(a179))),
% 0.79/0.99 inference(modus_ponens,[status(thm)],[2573, 2572])).
% 0.79/0.99 tff(2575,plain,
% 0.79/0.99 ($false),
% 0.79/0.99 inference(unit_resolution,[status(thm)],[2574, 175, 2568, 2543, 2567, 2566, 2565, 2005, 2004, 2003, 258, 2554])).
% 0.79/0.99 % SZS output end Proof
% 0.79/1.00 % E exiting
%------------------------------------------------------------------------------